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Probability · Class 10 Mathematics: 117 MCQs with answers

All 117 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 44 Quick Revision · 34

Warm-up · 32 questions

Q1. The classical definition of probability is

Beginner
A $\frac{\text{favourable}}{\text{total}}$ B $\frac{\text{total}}{\text{favourable}}$ C favourable $\times$ total D favourable $-$ total
Show answer & explanation

$\frac{\text{favourable}}{\text{total}}$

Wanted over total.

Q2. That definition requires the outcomes to be

Beginner
A few in number B numerical C equally likely D independent
Show answer & explanation

equally likely

Otherwise no outcome may be counted the same as another.

Q3. An OUTCOME is

Beginner
A a collection of results B the total number of results C a probability D one possible result of the experiment
Show answer & explanation

one possible result of the experiment

A single result.

Q4. An EVENT is

Beginner
A a single outcome only B the total C the complement D a collection of outcomes
Show answer & explanation

a collection of outcomes

Anything you might ask about.

Q5. The probability of an even number on one fair die is

Beginner
A $\frac12$ B $\frac13$ C $\frac16$ D $\frac23$
Show answer & explanation

$\frac12$

Three of the six faces.

Q6. Every probability satisfies

Beginner
A $P(E) > 1$ B $0 \le P(E) \le 1$ C $P(E) < 0$ D $P(E) = 1$ always
Show answer & explanation

$0 \le P(E) \le 1$

A part cannot exceed the whole.

Q7. $P(E) = 0$ means the event is

Beginner
A certain B very unlikely C impossible D equally likely
Show answer & explanation

impossible

No outcome is favourable.

Q8. $P(E) = 1$ means the event is

Beginner
A impossible B certain C very likely D unlikely
Show answer & explanation

certain

Every outcome is favourable.

Q9. The probability of rolling a 7 on one ordinary die is

Beginner
A $\frac16$ B $\frac17$ C 1 D 0
Show answer & explanation

0

No face shows 7.

Q10. The probability of rolling a number less than 7 on one die is

Beginner
A 1 B $\frac56$ C $\frac67$ D 0
Show answer & explanation

1

All six faces qualify.

Q11. The complementary event $\bar{E}$ is

Beginner
A the same as $E$ B the event that $E$ does not happen C the impossible event D the certain event
Show answer & explanation

the event that $E$ does not happen

Everything else.

Q12. The complement rule states that

Beginner
A $P(\bar{E}) = P(E)$ B $P(\bar{E}) = \frac{1}{P(E)}$ C $P(\bar{E}) = 1 + P(E)$ D $P(\bar{E}) = 1 - P(E)$
Show answer & explanation

$P(\bar{E}) = 1 - P(E)$

The event happens or it does not.

Q13. Assertion (A): The probability of an event can never exceed 1. Reason (R): A probability is written either as a fraction or as a decimal.

Beginner
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

Both A and R are true, but R is not the correct explanation of A

Both are true, but how a probability is written does not bound it; the count of favourable outcomes does.

Q14. The answer $\frac{18}{36}$ should be written as

Beginner
A $\frac{18}{36}$ B $\frac{9}{18}$ C $\frac12$ D $18 : 36$
Show answer & explanation

$\frac12$

Lowest terms.

Q15. The first step in any probability question should be to

Beginner
A guess the answer B find the complement C list the outcomes D reduce the fraction
Show answer & explanation

list the outcomes

Almost every error is a counting error.

Q16. If $P(E) = 0.35$, then $P(\bar{E})$ is

Beginner
A 0.35 B 0.65 C 1.35 D 0.5
Show answer & explanation

0.65

$1 - 0.35$.

Q17. Which statement is true?

Beginner
A $P(E) + P(\bar{E}) = 1$ B $P(E) \times P(\bar{E}) = 1$ C $P(E) - P(\bar{E}) = 1$ D $P(E) = P(\bar{E})$ always
Show answer & explanation

$P(E) + P(\bar{E}) = 1$

The event happens or it does not.

Q18. Probability as a subject began with

Beginner
A a study of the weather B a theorem of Euclid C a card trick D a question about dividing the stakes of an unfinished game
Show answer & explanation

a question about dividing the stakes of an unfinished game

Two seventeenth-century gamblers.

Q19. State the classical definition of probability and the condition it requires.

Beginner
Show answer & explanation

—

Q20. Distinguish an outcome from an event, with an example from a single die.

Beginner
Show answer & explanation

—

Q21. The number of outcomes when $n$ coins are tossed is

Beginner
A $2n$ B $n^2$ C $n!$ D $2^n$
Show answer & explanation

$2^n$

Each coin doubles the count.

Q22. Three coins tossed together have how many outcomes?

Beginner
A six B eight C four D three
Show answer & explanation

eight

$2^3$.

Q23. Two dice have how many outcomes?

Beginner
A 21 B 12 C 36 D 6
Show answer & explanation

36

$6 \times 6$.

Q24. A DOUBLE on two dice means

Beginner
A both dice show the same number B the total is doubled C a total of 12 D two sixes
Show answer & explanation

both dice show the same number

(1,1) through (6,6).

Q25. A standard pack contains

Beginner
A 52 cards in 13 suits of 4 B 52 cards in 4 suits of 13 C 48 cards D 54 cards
Show answer & explanation

52 cards in 4 suits of 13

Four thirteens.

Q26. The red suits are

Beginner
A spades and clubs B hearts and spades C hearts and diamonds D clubs and diamonds
Show answer & explanation

hearts and diamonds

26 red cards in all.

Q27. How many red cards are in a pack?

Beginner
A 26 B 13 C 24 D 52
Show answer & explanation

26

Two suits of thirteen.

Q28. $P(\text{a heart})$ from a full pack is

Beginner
A $\frac{1}{13}$ B $\frac14$ C $\frac{1}{26}$ D $\frac{1}{52}$
Show answer & explanation

$\frac14$

$\frac{13}{52}$.

Q29. $P(\text{a king})$ from a full pack is

Beginner
A $\frac14$ B $\frac{1}{13}$ C $\frac{1}{26}$ D $\frac{1}{52}$
Show answer & explanation

$\frac{1}{13}$

$\frac{4}{52}$.

Q30. The first thing to write in any question of this topic is

Beginner
A the total number of outcomes B the answer C the complement D the reduced fraction
Show answer & explanation

the total number of outcomes

Adjusted for any removals.

Q31. A bag game needs a six to start. $P(\text{starting on the first throw})$ of one die is

Beginner
A $\frac56$ B $\frac{1}{36}$ C $\frac16$ D $\frac12$
Show answer & explanation

$\frac16$

One favourable face of six.

Q32. Describe the structure of a pack of cards, including colours and face cards.

Beginner
Show answer & explanation

—

Building up · 43 questions

Q33. A drawing pin tossed in the air illustrates

Intermediate
A an impossible event B a certain event C a fair experiment D two outcomes that are NOT equally likely
Show answer & explanation

two outcomes that are NOT equally likely

Point-up and point-down do not happen equally often.

Q34. Tossing two coins has how many equally likely outcomes?

Intermediate
A four B three C two D eight
Show answer & explanation

four

HH, HT, TH, TT.

Q35. An answer of $\frac76$ for a probability indicates

Intermediate
A an arithmetic mistake B a very likely event C a certain event D an impossible event
Show answer & explanation

an arithmetic mistake

No probability can exceed 1.

Q36. If $P(E) = \frac{3}{8}$, then $P(\bar{E})$ is

Intermediate
A $\frac58$ B $\frac38$ C $\frac83$ D $\frac18$
Show answer & explanation

$\frac58$

$1 - \frac38$.

Q37. The probability of drawing a king from a pack is $\frac{1}{13}$. The probability of not drawing one is

Intermediate
A $\frac{1}{13}$ B $\frac{13}{12}$ C $\frac{12}{13}$ D $\frac{4}{52}$
Show answer & explanation

$\frac{12}{13}$

$1 - \frac{1}{13}$.

Q38. The complement is worth using when

Intermediate
A the numbers are large B the outcomes are unequal C the event is harder to count than its opposite D the answer is a decimal
Show answer & explanation

the event is harder to count than its opposite

One short count instead of one long one.

Q39. Which word usually signals that the complement will be quicker?

Intermediate
A 'and' B 'equal' C 'not' D 'total'
Show answer & explanation

'not'

Along with 'at least' and 'none'.

Q40. The probabilities of all the outcomes of an experiment add to

Intermediate
A 0 B 1 C the number of outcomes D $\frac12$
Show answer & explanation

1

Something must happen.

Q41. Which of these is NOT an acceptable way to write a probability?

Intermediate
A $\frac16$ B '1 : 6' C 0.1667 D about 17%
Show answer & explanation

'1 : 6'

A ratio states odds, not a probability.

Q42. A bag has 5 red and 15 blue balls. The probability of drawing red is

Intermediate
A $\frac13$ B $\frac15$ C $\frac{5}{15}$ D $\frac14$
Show answer & explanation

$\frac14$

$\frac{5}{20}$, reduced.

Q43. For that same bag, the probability of not drawing red is

Intermediate
A $\frac14$ B $\frac{15}{5}$ C $\frac34$ D $\frac12$
Show answer & explanation

$\frac34$

$1 - \frac14$.

Q44. A weather forecast of '70% rain' expresses a probability of

Intermediate
A $\frac{7}{10}$ B $\frac{7}{100}$ C $70$ D $\frac{10}{7}$
Show answer & explanation

$\frac{7}{10}$

A percentage is a fraction out of 100.

Q45. Assertion (A): Listing the outcomes before counting prevents most errors in this chapter. Reason (R): Tossing two coins has four outcomes, not three, which is only obvious once they are written out.

Intermediate
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

Both A and R are true, and R is the correct explanation of A

The listing makes HT and TH visibly different.

Q46. A bag has 3 white and 9 black balls. $P(\text{white})$ is

Intermediate
A $\frac13$ B $\frac14$ C $\frac19$ D $\frac{3}{9}$
Show answer & explanation

$\frac14$

$\frac{3}{12}$, reduced.

Q47. Explain why tossing two coins has four outcomes rather than three, and find the probability of exactly one head.

Intermediate
Show answer & explanation

—

Q48. Prove that every probability lies between 0 and 1, and say what the two extremes mean.

Intermediate
Show answer & explanation

—

Q49. Define the complementary event and derive the complement rule.

Intermediate
Show answer & explanation

—

Q50. A bag contains 5 red and 15 blue balls. Find the probability of drawing a red ball, and of not drawing one.

Intermediate
Show answer & explanation

—

Q51. State the conventions for writing a probability, and give one form that is not acceptable.

Intermediate
Show answer & explanation

—

Q52. With three coins, $P(\text{no heads})$ is

Intermediate
A $\frac38$ B $\frac18$ C $\frac12$ D $\frac78$
Show answer & explanation

$\frac18$

Only TTT.

Q53. Are $(2,5)$ and $(5,2)$ the same outcome for two dice?

Intermediate
A no, the dice are distinguishable B yes, always C only if the dice match D only for a total of 7
Show answer & explanation

no, the dice are distinguishable

First die and second die are different positions.

Q54. How many ways can two dice total 7?

Intermediate
A five B four C seven D six
Show answer & explanation

six

(1,6), (2,5), (3,4), (4,3), (5,2), (6,1).

Q55. $P(\text{total } 6)$ for two dice is

Intermediate
A $\frac16$ B $\frac{1}{36}$ C $\frac{5}{36}$ D $\frac{6}{36}$
Show answer & explanation

$\frac{5}{36}$

Five ways: (1,5), (2,4), (3,3), (4,2), (5,1).

Q56. $P(\text{total } 12)$ for two dice is

Intermediate
A $\frac16$ B $\frac{1}{12}$ C $\frac{1}{36}$ D $\frac{2}{36}$
Show answer & explanation

$\frac{1}{36}$

Only (6,6).

Q57. Which total is the most likely on two dice?

Intermediate
A 6 B 12 C 2 D 7
Show answer & explanation

7

It can be made in six ways.

Q58. $P(\text{a double})$ on two dice is

Intermediate
A $\frac{1}{36}$ B $\frac{1}{12}$ C $\frac16$ D $\frac{6}{12}$
Show answer & explanation

$\frac16$

Six of the thirty-six outcomes.

Q59. The face cards are

Intermediate
A the ace, jack and queen B the ace, king and queen C all the picture and ace cards D the jack, queen and king
Show answer & explanation

the jack, queen and king

Three per suit.

Q60. How many face cards are in a pack?

Intermediate
A 16 B 4 C 12 D 13
Show answer & explanation

12

Three per suit, four suits.

Q61. Assertion (A): An ace is a face card. Reason (R): The face cards of a pack are the jack, the queen and the king.

Intermediate
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

A is false but R is true

R is true and is exactly why A is false: the ace is not among them.

Q62. Assertion (A): Two dice give 36 equally likely outcomes. Reason (R): Each die has 6 faces and the two dice are distinguishable.

Intermediate
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

Both A and R are true, and R is the correct explanation of A

$6 \times 6$ ordered pairs, all equally likely.

Q63. $P(\text{a red king})$ is

Intermediate
A $\frac{1}{26}$ B $\frac{1}{13}$ C $\frac{1}{52}$ D $\frac14$
Show answer & explanation

$\frac{1}{26}$

Two cards out of 52.

Q64. $P(\text{a face card})$ is

Intermediate
A $\frac{1}{13}$ B $\frac14$ C $\frac{4}{13}$ D $\frac{3}{13}$
Show answer & explanation

$\frac{3}{13}$

$\frac{12}{52}$.

Q65. $P(\text{the queen of spades})$ is

Intermediate
A $\frac{1}{52}$ B $\frac{1}{13}$ C $\frac14$ D $\frac{1}{26}$
Show answer & explanation

$\frac{1}{52}$

Exactly one card.

Q66. All the face cards are removed from a pack. How many cards remain?

Intermediate
A 48 B 40 C 39 D 52
Show answer & explanation

40

$52 - 12$.

Q67. When cards are removed before a draw, you must adjust

Intermediate
A only the favourable count B only the total C neither D both the favourable count and the total
Show answer & explanation

both the favourable count and the total

Using 52 afterwards is the commonest error here.

Q68. 'At least one head' when three coins are tossed means

Intermediate
A exactly one head B two or more heads C no heads D one, two or three heads
Show answer & explanation

one, two or three heads

One or more.

Q69. Two dice are thrown. $P(\text{the same number on both})$ is

Intermediate
A $\frac{1}{36}$ B $\frac{1}{12}$ C $\frac16$ D $\frac12$
Show answer & explanation

$\frac16$

That is a double.

Q70. Two dice are thrown. $P(\text{a total of 1})$ is

Intermediate
A $\frac{1}{36}$ B $\frac16$ C 0 D 1
Show answer & explanation

0

The smallest possible total is 2.

Q71. Two coins are tossed. $P(\text{at least one tail})$ is

Intermediate
A $\frac12$ B $\frac34$ C $\frac14$ D $\frac23$
Show answer & explanation

$\frac34$

$1 - P(HH) = 1 - \frac14$.

Q72. List the outcomes when three coins are tossed, and find the probability of exactly two heads.

Intermediate
Show answer & explanation

—

Q73. For the same three coins, find the probability of at least one head, and say why the complement is quicker.

Intermediate
Show answer & explanation

—

Q74. For two dice, find the probability of a total of 7, of 12, and of a double.

Intermediate
Show answer & explanation

—

Q75. Find the probability of drawing a heart, a king, a red king and a face card from a full pack.

Intermediate
Show answer & explanation

—

Topper level · 42 questions

Q76. The probability of exactly one head when two coins are tossed is

Advanced
A $\frac13$ B $\frac14$ C $\frac23$ D $\frac12$
Show answer & explanation

$\frac12$

HT and TH, so $\frac24$.

Q77. Calling that probability $\frac13$ is wrong because

Advanced
A there are three coins B the coins are biased C 'one of each' happens in two ways, not one D it should be $\frac14$
Show answer & explanation

'one of each' happens in two ways, not one

HT and TH are different outcomes.

Q78. Two dice are thrown. The probability that the total is 7 is

Advanced
A $\frac16$ B $\frac{1}{36}$ C $\frac{7}{36}$ D $\frac{1}{12}$
Show answer & explanation

$\frac16$

Six of the thirty-six pairs total 7.

Q79. Assertion (A): An event with a very small probability is impossible. Reason (R): An event is impossible exactly when its probability is 0.

Advanced
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

A is false but R is true

R is true and is why A is false: small is not zero.

Q80. Two dice are thrown. The probability of a total other than 7 is

Advanced
A $\frac16$ B $\frac56$ C $\frac{1}{30}$ D $\frac{7}{36}$
Show answer & explanation

$\frac56$

$1 - \frac16$, using the complement.

Q81. If a list of probabilities does not add to 1, then

Advanced
A the experiment is unfair B the answer is still acceptable C the total is 2 D one is wrong or an outcome was missed
Show answer & explanation

one is wrong or an outcome was missed

It is a free check on the whole question.

Q82. 'At least one head' differs from 'exactly one head' because

Advanced
A they are the same B 'at least one' also includes two heads C 'at least one' excludes HT D 'exactly one' includes TT
Show answer & explanation

'at least one' also includes two heads

Read the phrase before counting.

Q83. A box holds 20 bulbs, 4 of them defective. The probability that one chosen at random is good is

Advanced
A $\frac15$ B $\frac{4}{20}$ C $\frac45$ D $\frac{16}{4}$
Show answer & explanation

$\frac45$

$1 - \frac{4}{20} = 1 - \frac15$.

Q84. A fair die is rolled. $P(\text{a factor of } 6)$ is

Advanced
A $\frac12$ B $\frac16$ C $\frac23$ D $\frac13$
Show answer & explanation

$\frac23$

The factors of 6 among 1 to 6 are 1, 2, 3 and 6 — four faces.

Q85. A fair die is rolled. $P(\text{a prime number})$ is

Advanced
A $\frac12$ B $\frac13$ C $\frac23$ D $\frac16$
Show answer & explanation

$\frac12$

The primes among 1 to 6 are 2, 3 and 5.

Q86. Saying an experiment is 'random' means

Advanced
A the result cannot be predicted at all B every outcome is equally likely C the outcomes are numerical D there are two outcomes
Show answer & explanation

every outcome is equally likely

It is a statement about balance, not about ignorance.

Q87. Assertion (A): A probability may be written as a ratio such as 1 : 6. Reason (R): A probability is a number between 0 and 1.

Advanced
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

A is false but R is true

R is true and shows A false: a ratio is not such a number, and 1 : 6 is odds, not a probability.

Q88. Two dice are thrown. Find the probability that the total is not 7, and explain why the complement is the quicker route.

Advanced
Show answer & explanation

—

Q89. Explain the difference between 'at least one head' and 'exactly one head' when two coins are tossed, and find both probabilities.

Advanced
Show answer & explanation

—

Q90. Explain why an event with a very small probability is not the same as an impossible one.

Advanced
Show answer & explanation

—

Q91. (a) State the classical definition of probability and the condition it requires, with an example where the condition fails. (b) Two coins are tossed. List the outcomes and find the probability of exactly one head, of at least one head, and of no heads. (c) Check that your three answers are consistent.

Advanced
Show answer & explanation

—

Q92. (a) Prove that $0 \le P(E) \le 1$ and explain the meaning of each extreme. (b) Derive the complement rule. (c) A box contains 20 bulbs, 4 of which are defective. Find the probability that a bulb drawn at random is good, by two different methods.

Advanced
Show answer & explanation

—

Q93. (a) Explain when the complement is worth using, and name the words that usually signal it. (b) Two dice are thrown. Find the probability that the total is 7, and hence that it is not 7. (c) Explain why listing the outcomes is the safest first step in this chapter.

Advanced
Show answer & explanation

—

Q94. (a) Explain the difference between an outcome and an event, and between 'at least one' and 'exactly one'. (b) A bag contains 3 white and 9 black balls. Find the probability of drawing a white ball, and of drawing one that is not white. (c) Explain how the fact that all probabilities sum to 1 can be used as a check.

Advanced
Show answer & explanation

—

Q95. With three coins, $P(\text{exactly two heads})$ is

Advanced
A $\frac38$ B $\frac14$ C $\frac18$ D $\frac12$
Show answer & explanation

$\frac38$

HHT, HTH and THH.

Q96. With three coins, $P(\text{at least one head})$ is

Advanced
A $\frac38$ B $\frac78$ C $\frac12$ D $\frac18$
Show answer & explanation

$\frac78$

$1 - \frac18$, since only TTT has no head.

Q97. For three coins, the head-counts 0, 1, 2 and 3 are

Advanced
A not equally likely B equally likely C impossible D all certain
Show answer & explanation

not equally likely

One head happens three ways, three heads only one.

Q98. Treating $(2,5)$ and $(5,2)$ as one outcome would give a total of

Advanced
A 36 outcomes B 21 outcomes instead of 36 C 12 outcomes D 30 outcomes
Show answer & explanation

21 outcomes instead of 36

And every later answer would be wrong.

Q99. How many cards are either an ace or a face card?

Advanced
A 16 B 12 C 4 D 17
Show answer & explanation

16

12 face cards plus 4 aces, with no overlap.

Q100. How many cards are a king OR a heart?

Advanced
A 17 B 16 C 13 D 4
Show answer & explanation

16

4 kings and 13 hearts, but the king of hearts is in both lists.

Q101. Adding 4 and 13 to answer that question gives 17, which is wrong because

Advanced
A the king of hearts would be counted twice B there are only 13 hearts C kings are not cards D the total is 52
Show answer & explanation

the king of hearts would be counted twice

Overlapping descriptions must not simply be added.

Q102. After that removal, how many hearts remain?

Advanced
A 13 B 12 C 9 D 10
Show answer & explanation

10

The hearts lose their jack, queen and king.

Q103. After that removal, $P(\text{a heart})$ is

Advanced
A $\frac{13}{40}$ B $\frac{1}{13}$ C $\frac{10}{52}$ D $\frac14$
Show answer & explanation

$\frac14$

$\frac{10}{40}$ — the removal was symmetric across the suits.

Q104. Which method is quicker for 'at least one head' with three coins?

Advanced
A listing all seven outcomes B the complement C the 36-outcome grid D neither works
Show answer & explanation

the complement

Only TTT fails, so one count replaces seven.

Q105. Two dice are thrown. $P(\text{a total of at least 11})$ is

Advanced
A $\frac{1}{36}$ B $\frac16$ C $\frac{1}{12}$ D $\frac{1}{18}$
Show answer & explanation

$\frac{1}{12}$

Totals 11 and 12 give $2 + 1 = 3$ outcomes, so $\frac{3}{36}$.

Q106. One card is drawn from a pack. $P(\text{a black face card})$ is

Advanced
A $\frac{3}{13}$ B $\frac{1}{26}$ C $\frac{3}{26}$ D $\frac{6}{13}$
Show answer & explanation

$\frac{3}{26}$

Six such cards out of 52.

Q107. Assertion (A): Removing cards from a pack changes only the favourable count. Reason (R): The probability is the favourable count divided by the total number of cards available.

Advanced
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

A is false but R is true

R is true and shows A false: the total available has changed as well.

Q108. Assertion (A): With two dice, a total of 7 is less likely than a double. Reason (R): Each can happen in six of the thirty-six outcomes.

Advanced
A Both A and R are true, and R is the correct explanation of A B Both A and R are true, but R is not the correct explanation of A C A is true but R is false D A is false but R is true
Show answer & explanation

A is false but R is true

Each happens in six of the thirty-six outcomes, so they are equally likely and the assertion is false. The reason gives the counts.

Q109. Explain why two dice give 36 outcomes rather than 21, and why it matters.

Advanced
Show answer & explanation

—

Q110. How many cards in a pack are a king or a heart? Explain why the answer is not 17.

Advanced
Show answer & explanation

—

Q111. All the face cards are removed from a pack and one card is drawn. Find the probability that it is a heart.

Advanced
Show answer & explanation

—

Q112. Explain why the head-counts 0, 1, 2 and 3 are not equally likely for three coins.

Advanced
Show answer & explanation

—

Q113. Two dice are thrown. Find the probability that the total is at least 11.

Advanced
Show answer & explanation

—

Q114. (a) Explain why $n$ coins give $2^n$ outcomes, and list those for three coins. (b) Find the probability of exactly two heads, at least one head, and no heads. (c) Explain why the four possible head-counts are not equally likely.

Advanced
Show answer & explanation

—

Q115. (a) Explain why two dice give 36 outcomes and why using 21 would be wrong. (b) Give the number of ways of making each total from 2 to 12. (c) Hence find the probability of a total of 7, of 12, and of at least 11.

Advanced
Show answer & explanation

—

Q116. (a) Describe a pack of cards fully: suits, colours, ranks and face cards. (b) Find the probability of drawing a heart, a king, a red king and a black face card. (c) Explain why 'a king or a heart' is 16 cards rather than 17.

Advanced
Show answer & explanation

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Q117. (a) Explain what must change when cards are removed from a pack before a draw. (b) All the face cards are removed and one card is drawn. Find the probability that it is a heart, and that it is a king. (c) Explain why the first answer is unchanged from the full pack while the second is not.

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