Pariksha SaathiQuantitative Aptitude
Probability — Tier II: Practice Questions with Answers
15 practice questions on Probability — Tier II, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
Two coins are tossed together. Find the probability of getting at least one head.
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Answer: 3/4
Solution:
- Total outcomes: HH, HT, TH, TT — 4 in all.
- It’s easier to find the opposite first: P(no heads) = P(TT) = 1/4.
- P(at least one head) = 1 − 1/4 = 3/4.
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Q.2
A die is rolled once. Find the probability of getting a number greater than 4.
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Answer: 1/3
Solution:
- Numbers greater than 4 on a standard die: 5 and 6 — that’s 2 favorable outcomes out of 6 total.
- Probability = 2/6 = 1/3.
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Q.3
A bag contains 4 red balls and 6 green balls. Two balls are drawn at random together. Find the probability that both are red.
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Answer: 2/15
Solution:
- Drawing 2 balls together is a selection, so count with combinations.
- Total ways to choose any 2 from 10: ¹⁰C₂ = 45. Favorable ways to choose 2 red from 4: ⁴C₂ = 6.
- Probability = 6/45 = 2/15.
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Q.4
A coin is tossed and a die is rolled together. Find the probability of getting a head on the coin AND a number greater than 4 on the die.
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Answer: 1/6
Solution:
- These are independent events. P(head) = 1/2. P(number > 4) = 2/6 = 1/3.
- P(both) = P(head) × P(number > 4) = (1/2) × (1/3)
- = 1/6
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Q.5
A bag contains 5 red balls and 3 blue balls. One ball is drawn at random. Find the probability that it is blue.
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Answer: 3/8
Solution:
- Total balls = 5 + 3 = 8. Favorable outcomes (blue) = 3.
- Probability = 3/8.
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Q.6
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.
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Answer: 2/13
Solution:
- There are 4 Kings and 4 Queens, and a single card can’t be both — these are mutually exclusive.
- P(King or Queen) = 4/52 + 4/52 = 8/52 = 2/13.
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Q.7
The same bag (4 red, 6 green) is used, but now 2 balls are drawn one after another WITHOUT replacement. Find the probability that both are red, and check it against the previous answer.
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Answer: 2/15
Solution:
- P(first red) = 4/10. Given the first was red, 3 red remain out of 9 total, so P(second red) = 3/9.
- P(both red) = (4/10) × (3/9) = 12/90 = 2/15.
- This matches the combination-based answer from the previous example, as it should — both methods describe the same situation.
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Q.8
Two dice are rolled together. Find the probability that the sum of the two numbers is 7.
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Answer: 1/6
Solution:
- Total equally likely outcomes = 6 × 6 = 36.
- Pairs that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — 6 favorable outcomes.
- Probability = 6/36 = 1/6.
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Q.9
A coin is tossed and a card is drawn from a standard deck. Find the probability of getting a tail and a King.
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Q.10
A bag contains 3 red and 5 blue balls. Two balls are drawn one after another without replacement. Find the probability that both are blue.
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Q.11
A bag contains 3 red and 7 blue balls. Two balls are drawn together at random. Find the probability that both are blue.
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Q.12
Two dice are rolled together. Find the probability that the sum of the numbers is 10.
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Q.13
A die is rolled once. Find the probability of getting an even number.
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Q.14
A bag contains 4 white balls and 6 black balls. One ball is drawn at random. Find the probability that it is white.
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Q.15
Two coins are tossed together. Find the probability of getting exactly one head.
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.