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Probability Questions with Solutions

Probability questions almost always reduce to careful counting — list (or count) the favorable outcomes, list (or count) all possible outcomes, and divide. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

  • Probability of an event = (number of favorable outcomes) / (total number of possible outcomes), assuming every outcome is equally likely. It’s always between 0 (impossible) and 1 (certain).
  • For two events that can’t both happen (mutually exclusive), the probability that EITHER happens is the sum: P(A or B) = P(A) + P(B).
  • For two INDEPENDENT events (one doesn’t affect the other), the probability that BOTH happen is the product: P(A and B) = P(A) × P(B).
  • For "at least one" questions, it’s usually easier to find the probability of the opposite (none happen) and subtract from 1: P(at least one) = 1 − P(none).

Worked examples

1. A die is rolled once. Find the probability of getting a number greater than 4.

Solution

  1. Numbers greater than 4 on a standard die: 5 and 6 — that’s 2 favorable outcomes out of 6 total.
  2. Probability = 2/6 = 1/3.

Answer: 1/3

2. A bag contains 5 red balls and 3 blue balls. One ball is drawn at random. Find the probability that it is blue.

Solution

  1. Total balls = 5 + 3 = 8. Favorable outcomes (blue) = 3.
  2. Probability = 3/8.

Answer: 3/8

3. Two coins are tossed together. Find the probability of getting at least one head.

Solution

  1. Total outcomes: HH, HT, TH, TT — 4 in all.
  2. It’s easier to find the opposite first: P(no heads) = P(TT) = 1/4.
  3. P(at least one head) = 1 − 1/4 = 3/4.

Answer: 3/4

4. A card is drawn at random from a standard deck of 52 playing cards. Find the probability that it is either a King or a Queen.

Solution

  1. There are 4 Kings and 4 Queens, and a single card can’t be both — these are mutually exclusive.
  2. P(King or Queen) = 4/52 + 4/52 = 8/52 = 2/13.

Answer: 2/13

Try these yourself

Work through these the same way, then check against the answer.

1. A die is rolled once. Find the probability of getting an even number.

Answer: 1/2

2. A bag contains 4 white balls and 6 black balls. One ball is drawn at random. Find the probability that it is white.

Answer: 2/5

3. Two coins are tossed together. Find the probability of getting exactly one head.

Answer: 1/2

Where this comes up

Probability is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and builds directly on Permutation and Combination.

Practice more Probability questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Probability (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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