68 practice questions on Probability (Class 11), sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Probability (Class 11) notes.
📐 Mathematics · Class 11 · JEE
Probability (Class 11) - Practice Questions with Answers
68 free MCQs on Probability (Class 11), each with its own worked answer and explanation. Random experiments, sample space, events, and the axiomatic approach to probability
Take the timed Probability (Class 11) chapterwise test →Easy - 20 questions
Q1.
The set of all possible outcomes of a random experiment is called the:
- A Sample space
- B Outcome pair
- C Trial
- D Event
Q2.
When a single coin is tossed, the number of elements in the sample space is:
- A 1
- B 2
- C 4
- D 8
Q3.
When two coins are tossed together, the number of possible outcomes is:
- A 2
- B 3
- C 4
- D 8
Q6.
The probability of any event A always satisfies:
- A P(A) ≥ 1
- B 0 ≤ P(A) ≤ 1
- C −1 ≤ P(A) ≤ 1
- D P(A) > 1
Q7.
When a die is rolled once, the probability of getting a 4 is:
- A 1/2
- B 1/3
- C 1/6
- D 4/6
Q8.
When a die is rolled once, the probability of getting an even number is:
- A 2/3
- B 1/6
- C 1/3
- D 1/2
Q10.
Two events A and B are mutually exclusive if:
- A P(A) = P(B)
- B A ∩ B = ∅
- C A ∪ B = S
- D A = B
Q11.
An event consisting of exactly one sample point is called a:
- A Sure event
- B Impossible event
- C Simple event
- D Compound event
Q12.
When two dice are thrown, the total number of outcomes is:
- A 72
- B 12
- C 24
- D 36
Q13.
A card is drawn from a standard pack of 52. The probability that it is a heart is:
- A 1/4
- B 1/2
- C 1/52
- D 1/13
Q14.
A card is drawn from a standard pack. The probability that it is a king is:
- A 1/52
- B 1/13
- C 1/4
- D 4/13
Q15.
When three coins are tossed, the number of elements in the sample space is:
- A 3
- B 6
- C 8
- D 9
Q16.
For mutually exclusive events A and B, P(A ∪ B) equals:
- A P(A) × P(B)
- B P(A) − P(B)
- C P(A) + P(B) − 1
- D P(A) + P(B)
Q17.
An event that contains more than one sample point is called a:
- A Compound event
- B Simple event
- C Null event
- D Sure event
Q18.
The complement of the event 'getting a head' when one coin is tossed is:
- A The impossible event
- B Getting a tail
- C Getting a head again
- D The sure event
Q19.
When a die is rolled, the probability of getting a number greater than 6 is:
- A 1
- B 1/2
- C 0
- D 1/6
Q20.
If a bag has 3 red and 2 blue balls, the probability of drawing a red ball is:
- A 1/2
- B 3/2
- C 2/5
- D 3/5
Medium - 20 questions
Q21.
Two dice are thrown. The probability that the sum is 8 is:
- A 5/36
- B 1/6
- C 4/36
- D 6/36
Q22.
Two dice are thrown. The probability of getting a doublet is:
- A 5/36
- B 1/6
- C 1/12
- D 1/36
Q23.
Three coins are tossed. The probability of getting at least one head is:
- A 3/8
- B 1/2
- C 7/8
- D 1/8
Q24.
A card is drawn from a pack. The probability that it is a king or a heart is:
- A 17/52
- B 1/13
- C 16/13
- D 4/13
Q25.
If P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2, then P(A ∪ B) is:
- A 0.7
- B 0.9
- C 1.1
- D 0.3
Q26.
Two dice are thrown. The probability that the sum is greater than 10 is:
- A 2/9
- B 1/12
- C 1/6
- D 1/9
Q27.
A number is chosen at random from 1 to 25. The probability that it is a multiple of 5 is:
- A 5/24
- B 4/25
- C 1/5
- D 1/25
Q28.
A card is drawn from a pack. The probability that it is a face card is:
- A 1/13
- B 4/13
- C 1/4
- D 3/13
Q29.
Two coins are tossed. The probability of getting exactly one head is:
- A 1/2
- B 1/4
- C 3/4
- D 1/3
Q30.
If the odds in favour of an event are 3 : 2, the probability of the event is:
- A 2/3
- B 3/5
- C 2/5
- D 3/2
Q31.
A bag contains 5 red and 7 white balls. One ball is drawn. The probability that it is white is:
- A 7/5
- B 1/2
- C 7/12
- D 5/12
Q32.
Two dice are thrown. The probability that the sum is a prime number is:
- A 1/3
- B 7/18
- C 1/2
- D 5/12
Q33.
If A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.45, then P(A ∪ B) is:
- A 0.75
- B 0.15
- C 0.135
- D 1
Q34.
A letter is chosen at random from the word ASSASSINATION. The probability that it is a vowel is:
- A 1/2
- B 6/13
- C 7/13
- D 5/13
Q35.
Two dice are thrown. The probability that both show the same number is:
- A 5/36
- B 1/3
- C 1/6
- D 1/36
Q36.
If P(A) = 0.6 and P(A ∩ B) = 0.25, the probability that A occurs but B does not is:
- A 0.85
- B 0.25
- C 0.15
- D 0.35
Q37.
A card is drawn from a pack. The probability that it is neither a heart nor a king is:
- A 9/13
- B 4/13
- C 3/13
- D 1/2
Q38.
Two dice are thrown. The probability that the sum is 7 is:
- A 1/12
- B 1/6
- C 5/36
- D 1/9
Q39.
One number is chosen from 1 to 100. The probability that it is a perfect square is:
- A 1/50
- B 9/100
- C 1/10
- D 1/100
Q40.
If P(A) = 0.5, P(B) = 0.4 and P(A ∪ B) = 0.7, then P(A ∩ B) is:
- A 0.1
- B 0.3
- C 0.9
- D 0.2
Hard - 28 questions
Q41.
Why is 'mutually exclusive' not the same as 'exhaustive'?
- A Mutually exclusive means the events cannot overlap; exhaustive means together they cover the whole sample space
- B The two terms describe identical conditions expressed in different words
- C Mutually exclusive events must always be equally likely as well
- D Exhaustive events must always have equal probabilities in every case
Q42.
When two dice are rolled, why is treating (2, 3) and (3, 2) as a single outcome an error?
- A Unordered pairs are correct, but the arithmetic becomes harder to manage
- B The two dice are distinguishable, so the resulting 21 unordered pairs are not equally likely
- C Ordered pairs are only used when the dice have different numbers of faces
- D The sample space must always contain exactly 36 elements by definition
Q43.
The formula P(A) = n(A)/n(S) is valid only when:
- A The event A is a simple event containing one outcome
- B The events under consideration are mutually exclusive
- C All outcomes in the sample space are equally likely
- D The sample space contains a finite number of outcomes only
Q44.
Four cards are drawn from a pack. The probability that all four are kings is:
- A 1/13²
- B 4/52
- C 1/2704
- D 1/270725
Q45.
Three cards are drawn from a pack. The probability that all three are hearts is:
- A 11/850
- B 1/64
- C 13/52
- D 3/13
Q46.
If A and B are events with P(A) = 0.5, P(B) = 0.3, what is the largest possible value of P(A ∩ B)?
- A 0.15
- B 0.3
- C 0.5
- D 0.8
Q47.
Two dice are thrown. The probability that the sum is neither 7 nor 11 is:
- A 1/6
- B 5/6
- C 7/9
- D 2/9
Q48.
A committee of 3 is chosen from 5 men and 4 women. The probability that it has exactly 2 women is:
- A 3/14
- B 1/2
- C 10/21
- D 5/14
Q49.
Why does the addition rule subtract P(A ∩ B)?
- A Outcomes lying in both events would otherwise be counted twice in P(A) + P(B)
- B The intersection always has probability zero and must be removed
- C Subtraction converts the union into a mutually exclusive pair of events
- D Probabilities must sum to exactly one across all events considered
Q50.
Two cards are drawn without replacement. The probability that both are aces is:
- A 4/52
- B 1/221
- C 1/169
- D 1/13
Q51.
Six people sit in a row at random. The probability that two particular people sit together is:
- A 2/5
- B 1/2
- C 1/3
- D 1/6
Q52.
If the odds against an event are 5 : 3, the probability of the event is:
- A 5/8
- B 3/5
- C 5/3
- D 3/8
Q53.
A number is chosen from 1 to 20. The probability that it is divisible by 3 or 5 is:
- A 9/20
- B 1/2
- C 2/5
- D 11/20
Q54.
Why is P(at least one) usually computed via the complement?
- A The complement always produces a larger and therefore safer probability value
- B The complement 'none' is a single scenario, while 'at least one' splits into many separate cases
- C The complement rule is the only exact method available for such events
- D 'At least one' events are always impossible to count directly in principle
Q55.
Three dice are thrown. The probability that all three show the same number is:
- A 1/6
- B 6/216
- C 1/36
- D 1/216
Q56.
Two events A and B satisfy P(A) = 0.4, P(B) = 0.7 and P(A ∪ B) = 1. What is P(A ∩ B)?
- A 0.3
- B 0.28
- C 0
- D 0.1
Q57.
From a pack of 52, one card is drawn. The probability that it is a red face card is:
- A 3/26
- B 3/13
- C 1/26
- D 6/13
Q58.
Four coins are tossed. The probability of getting exactly two heads is:
- A 5/16
- B 3/8
- C 1/4
- D 1/2
Q59.
If A ⊆ B, then which relation must hold?
- A P(A) = P(B) always
- B P(A) + P(B) = 1
- C P(A) ≤ P(B)
- D P(A) ≥ P(B)
Q60.
Two dice are thrown. Given the sample space of 36 equally likely outcomes, the sum with the highest probability is:
- A 6
- B 8
- C 12
- D 7
Q61.
A card is drawn from a standard deck. The probability it is a face card is:
- A 3/13
- B 1/13
- C 4/13
- D 12/13
Q62.
Two fair dice are thrown. The probability that the sum is a prime number is:
- A 5/12
- B 1/3
- C 1/2
- D 7/18
Q63.
The letters A, B, C, D are arranged at random in a row. The probability that A comes before B is:
- A 1/4
- B 1/2
- C 1/3
- D 3/4
Q64.
Two cards are drawn from a standard deck without replacement. The probability that both are aces is:
- A 1/221
- B 1/169
- C 2/221
- D 1/13
Q65.
If A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.4, then P(A ∪ B) equals:
- A 0.12
- B 0.7
- C 0.1
- D 1
Q66.
If the odds in favour of an event are 3 : 2, the probability of the event is:
- A 2/5
- B 3/5
- C 3/2
- D 2/3
Q67.
A number is chosen at random from 1 to 20. The probability it is divisible by 3 or 5 is:
- A 9/20
- B 1/2
- C 7/20
- D 11/20
Q68.
Three fair coins are tossed. The probability of getting at least two tails is:
- A 3/8
- B 1/2
- C 1/4
- D 5/8
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