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Probability practice questions for bank exams
Probability measures how likely an event is, as favourable outcomes divided by total outcomes. A probability is always between 0 and 1. Bank-exam questions stay close to dice, coins, cards and bags of coloured balls, so the work is mostly careful counting. The five questions below are at prelims-to-mains level.
What to know
| Idea | Rule |
|---|---|
| Probability of an event | Favourable outcomes ÷ total outcomes |
| Complement | P(not E) = 1 − P(E) |
| "Or" for any events | P(A or B) = P(A) + P(B) − P(A and B) |
| "And" for independent events | P(A and B) = P(A) × P(B) |
| Drawing from a bag | Count with combinations: nCr favourable ÷ nCr total |
| Without replacement | Each draw changes the bag, so use combinations or conditional fractions |
The number of ways to get each sum with two dice is worth learning, because dice questions are common.
| Sum | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ways (out of 36) | 1 | 2 | 3 | 4 | 5 | 6 | 5 | 4 | 3 | 2 | 1 |
Five practice questions
Question 1
Two fair dice are thrown together. What is the probability that the sum of the numbers is 8?
- A. 1/6
- B. 5/36
- C. 7/36
- D. 5/18
Question 2
A bag has 4 red, 5 blue and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both are blue?
- A. 5/33
- B. 10/33
- C. 25/144
- D. 5/12
Question 3
Three fair coins are tossed together. What is the probability of getting at least two heads?
- A. 1/4
- B. 3/8
- C. 1/2
- D. 5/8
Question 4
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a king or a heart?
- A. 17/52
- B. 4/13
- C. 1/4
- D. 3/13
Question 5
A and B try to solve a problem independently. The probability that A solves it is 1/3 and the probability that B solves it is 1/4. What is the probability that exactly one of them solves it?
- A. 5/12
- B. 1/2
- C. 7/12
- D. 11/12
Answers and explanations
- B. The favourable pairs are (2,6), (3,5), (4,4), (5,3) and (6,2), which is 5 of 36 outcomes. The probability is 5/36.
- A. There are 12 balls in all. The number of ways to choose 2 blue balls is 5C2 = 10, and the total ways to choose any 2 are 12C2 = 66. The probability is 10/66 = 5/33. The option 25/144 is the answer if the first ball were replaced.
- C. The favourable outcomes are HHT, HTH, THH and HHH, which is 4 of the 8 equally likely outcomes. The probability is 4/8 = 1/2.
- B. There are 4 kings and 13 hearts, but the king of hearts is in both groups. The count is 4 + 13 − 1 = 16 cards, so the probability is 16/52 = 4/13. The option 17/52 double counts the king of hearts.
- A. Only A solves: 1/3 × (1 − 1/4) = 1/3 × 3/4 = 1/4. Only B solves: (1 − 1/3) × 1/4 = 2/3 × 1/4 = 1/6. The total is 1/4 + 1/6 = 5/12. The option 1/2 is the probability that at least one solves it.
How to prepare probability
- Write the sample space size first. Dice pairs give 36, three coins give 8, and a card pack gives 52. A wrong denominator spoils everything else.
- Use combinations for bag questions. Choosing the two balls together with nCr is quicker than multiplying conditional fractions, and the two methods give the same answer.
- Spot "at least" and use the complement. For "at least one", find 1 − P(none).
- Respect overlaps. Questions with "or" often have a shared case, as in the king of hearts.
- Keep independent and dependent apart. Multiply plain probabilities only when the events do not affect each other, and adjust the second fraction when there is no replacement.
- Simplify at the end. Keep fractions unreduced while multiplying, then cancel once.
Allow 45 to 60 seconds. If you need more practice with counting, first revisit permutation and combination.
The full probability topic test is on PrepMatic (about 15 questions, 30 minutes). The Quantitative Aptitude guide shows how this topic relates to the rest of Quant, and the bank exam hub links each exam's pattern.
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