Probability questions

Aptitude Updated 11 Oct 2026

These probability questions cover the topics most often asked in aptitude tests: coins, dice, playing cards, balls drawn from a bag and simple independent events. There are 30 probability aptitude questions with answers, arranged from basic to exam level for SSC, bank, railway and campus placement tests.

Each answer comes with the working in a few short steps, so you can see how the total outcomes and favourable outcomes were counted. Try each question on paper first, then check the method in the explanation.

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Probability questions on coins

Q1. A fair coin is tossed once. What is the probability of getting a head?
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Answer: A. 1/2
There are 2 equally likely outcomes (H, T) and 1 is a head, so P = 1/2.
Q2. Two fair coins are tossed together. What is the probability of getting two heads?
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Answer: B. 1/4
Outcomes: HH, HT, TH, TT. Only HH has two heads, so P = 1/4.
Q3. Two coins are tossed. What is the probability of getting at least one head?
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Answer: D. 3/4
Only TT has no head. P(at least one head) = 1 minus 1/4 = 3/4.
Q4. Three coins are tossed. What is the probability of getting exactly two heads?
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Answer: C. 3/8
Total outcomes = 2^3 = 8. Exactly two heads: HHT, HTH, THH = 3. P = 3/8.
Q5. Three coins are tossed. What is the probability of getting at most one head?
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Answer: C. 1/2
No head: TTT (1). One head: HTT, THT, TTH (3). P = 4/8 = 1/2.
Q6. Four coins are tossed. What is the probability of getting exactly two heads?
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Answer: D. 3/8
Total outcomes = 2^4 = 16. Ways to get two heads = 4C2 = 6. P = 6/16 = 3/8.

Probability questions on dice

Q7. A fair die is rolled once. What is the probability of getting an even number?
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Answer: B. 1/2
Even numbers are 2, 4 and 6, which is 3 out of 6 outcomes. P = 3/6 = 1/2.
Q8. A die is rolled once. What is the probability of getting a prime number?
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Answer: A. 1/2
Primes on a die are 2, 3 and 5. P = 3/6 = 1/2. Note that 1 is not a prime number.
Q9. A die is rolled once. What is the probability of getting a number greater than 4?
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Answer: B. 1/3
Numbers greater than 4 are 5 and 6. P = 2/6 = 1/3.
Q10. Two dice are thrown together. What is the probability that the sum is 7?
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Answer: C. 1/6
Total outcomes = 36. Sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. P = 6/36 = 1/6.
Q11. Two dice are thrown. What is the probability of getting a doublet (the same number on both)?
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Answer: D. 1/6
Doublets are (1,1) to (6,6), which is 6 outcomes out of 36. P = 6/36 = 1/6.
Q12. Two dice are thrown. What is the probability that the sum of the numbers is 9?
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Answer: A. 1/9
Sum 9: (3,6), (4,5), (5,4), (6,3) = 4 outcomes. P = 4/36 = 1/9.
Q13. Two dice are thrown. What is the probability that the sum is greater than 9?
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Answer: D. 1/6
Sum 10: 3 ways, sum 11: 2 ways, sum 12: 1 way, total 6. P = 6/36 = 1/6.
Q14. Two dice are thrown. What is the probability that the product of the numbers is even?
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Answer: A. 3/4
The product is odd only when both are odd: 3 x 3 = 9 ways. P(even) = 1 minus 9/36 = 27/36 = 3/4.

Probability questions on playing cards

Q15. One card is drawn from a well shuffled pack of 52 cards. What is the probability that it is a king?
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Answer: B. 1/13
There are 4 kings in 52 cards. P = 4/52 = 1/13.
Q16. A card is drawn from a pack of 52 cards. What is the probability of getting a red card?
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Answer: C. 1/2
Hearts and diamonds give 26 red cards. P = 26/52 = 1/2.
Q17. A card is drawn from a pack of 52 cards. What is the probability that it is a face card (jack, queen or king)?
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Answer: B. 3/13
There are 3 face cards in each of 4 suits = 12. P = 12/52 = 3/13.
Q18. A card is drawn from a pack of 52 cards. What is the probability that it is a heart or a king?
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Answer: A. 4/13
Hearts = 13, kings = 4, king of hearts counted twice. Favourable = 13 + 4 minus 1 = 16. P = 16/52 = 4/13.
Q19. A card is drawn from a pack of 52 cards. What is the probability that it is a red face card?
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Answer: C. 3/26
Red suits have 3 face cards each, so 6 red face cards. P = 6/52 = 3/26.
Q20. Two cards are drawn together from a pack of 52 cards. What is the probability that both are aces?
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Answer: D. 1/221
Ways to pick 2 aces = 4C2 = 6. Ways to pick any 2 cards = 52C2 = 1326. P = 6/1326 = 1/221.

Balls and bags probability questions

Q21. A bag has 5 red and 3 blue balls. One ball is drawn at random. What is the probability that it is red?
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Answer: D. 5/8
Total balls = 5 + 3 = 8 and red balls = 5. P = 5/8.
Q22. A bag contains 4 white and 6 black balls. Two balls are drawn at random. What is the probability that both are white?
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Answer: C. 2/15
Ways to pick 2 white = 4C2 = 6. Total ways = 10C2 = 45. P = 6/45 = 2/15.
Q23. A bag has 3 red and 5 green balls. Two balls are drawn at random. What is the probability that one is red and one is green?
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Answer: A. 15/28
Favourable = 3C1 x 5C1 = 15. Total = 8C2 = 28. P = 15/28.
Q24. A box has 4 defective and 5 good bulbs. Three bulbs are picked at random. What is the probability that at least one is defective?
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Answer: B. 37/42
P(none defective) = 5C3 / 9C3 = 10/84 = 5/42. P(at least one defective) = 1 minus 5/42 = 37/42.
Q25. A bag has 2 red, 3 yellow and 4 blue marbles. One marble is drawn. What is the probability that it is neither yellow nor blue?
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Answer: C. 2/9
Neither yellow nor blue means red. There are 2 red out of 9 marbles. P = 2/9.
Q26. A bag has 6 green and 4 pink balls. Two balls are drawn one after another without replacement. What is the probability that both are green?
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Answer: A. 1/3
P(first green) = 6/10. P(second green) = 5/9. P = 6/10 x 5/9 = 30/90 = 1/3.

Mixed probability aptitude questions

Q27. A number is picked at random from 1 to 30. What is the probability that it is a multiple of 3 or 5?
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Answer: B. 7/15
Multiples of 3 = 10, of 5 = 6, of 15 = 2. Favourable = 10 + 6 minus 2 = 14. P = 14/30 = 7/15.
Q28. The probability that A hits a target is 1/4 and that B hits it is 2/3. If both shoot once independently, what is the probability that both hit the target?
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Answer: D. 1/6
For independent events, P(A and B) = P(A) x P(B) = 1/4 x 2/3 = 2/12 = 1/6.
Q29. A and B can hit a target with probabilities 1/4 and 2/3 respectively. If both shoot once, what is the probability that the target is hit?
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Answer: B. 3/4
P(both miss) = 3/4 x 1/3 = 1/4. P(target hit) = 1 minus 1/4 = 3/4.
Q30. The letters of the word LEAP are arranged at random. What is the probability that the arrangement begins with a vowel?
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Answer: C. 1/2
LEAP has 2 vowels (E, A) out of 4 letters, so any one letter is equally likely to be first. P = 2/4 = 1/2.
Q31. What is the probability that a leap year, chosen at random, has 53 Sundays?
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Answer: A. 2/7
A leap year has 52 weeks and 2 extra days. Of the 7 equally likely pairs of extra days, 2 contain a Sunday (Sat-Sun, Sun-Mon). P = 2/7.
Q32. If the probability of an event happening is 3/7, what is the probability that it does not happen?
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Answer: D. 4/7
P(not E) = 1 minus P(E) = 1 minus 3/7 = 4/7.

How to prepare

Every probability question uses one rule: P(event) = favourable outcomes divided by total outcomes. First count the sample space (2 for a coin, 6 for a die, 36 for two dice, 52 for a pack of cards, nCr when picking r items together). Then count only the outcomes that fit the condition and reduce the fraction.

Learn three shortcuts. For 'at least one', use 1 minus P(none). For 'A or B', add the two counts and subtract the overlap. For independent events, multiply the probabilities; for drawing without replacement, reduce both the favourable and total counts after each draw. Remember the card facts too: 26 red, 26 black, 13 in each suit, 4 of each rank and 12 face cards.

Study tips

Write the total number of outcomes first, before counting favourable cases, so you never divide by the wrong number.
For any question with 'at least one', find the probability of 'none' and subtract it from 1.
Memorise the sum table for two dice (sum 7 has 6 ways, sums 2 and 12 have 1 way each) to save time in exams.

Questions people ask

What is the formula for probability?

Probability of an event = number of favourable outcomes divided by total number of equally likely outcomes. Its value always lies between 0 and 1, and P(not E) = 1 minus P(E).

How do I solve probability aptitude questions quickly?

Identify the sample space first, then count favourable outcomes using combinations where items are picked together. Use 1 minus P(none) for 'at least one' questions and multiply probabilities for independent events.

What types of probability questions are asked in exams?

Exams mostly ask about coins, dice, playing cards, balls drawn from bags, and the chance that two independent events both happen. Placement tests also include questions on arranging letters and selecting people.

How many outcomes are there when two dice are thrown?

When two dice are thrown there are 6 x 6 = 36 equally likely outcomes. The most likely sum is 7, which can happen in 6 ways.

What are face cards in a pack of 52 cards?

The jack, queen and king of each suit are face cards, giving 12 face cards in all. Aces are not counted as face cards.

Every question on this page is written and fact-checked by the GK Quizzes team. Spotted a mistake? Tell us and we will fix it. How we make our questions.