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GATE Probability Questions with Answers & Explanations

18 Probability questions from the Engineering Mathematics section of GATE, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

Two fair dice are thrown. What is the probability that the sum of the numbers is 12?

  1. A1/12
  2. B1/36
  3. C1/6
  4. D1/18
Show answer
Answer: (B) 1/36 There are 1 favourable outcomes out of 36, so P = 1/36.
Question 2

Two fair dice are thrown. What is the probability that the sum of the numbers is 7?

  1. A1/6
  2. B7/36
  3. C5/36
  4. D1/2
Show answer
Answer: (A) 1/6 There are 6 favourable outcomes out of 36, so P = 1/6.
Question 3

Two fair dice are thrown. What is the probability that the sum of the numbers is 9?

  1. A1/9
  2. B1/12
  3. C1/3
  4. D5/36
Show answer
Answer: (A) 1/9 There are 4 favourable outcomes out of 36, so P = 1/9.
Question 4

Two fair dice are thrown. What is the probability that the sum of the numbers is 2?

  1. A1/6
  2. B1/36
  3. C1/18
  4. D1/12
Show answer
Answer: (B) 1/36 There are 1 favourable outcomes out of 36, so P = 1/36.
Question 5

Two fair dice are thrown. What is the probability that the sum of the numbers is 5?

  1. A1/9
  2. B1/12
  3. C1/3
  4. D1/6
Show answer
Answer: (A) 1/9 There are 4 favourable outcomes out of 36, so P = 1/9.
Question 6

Two fair dice are thrown. What is the probability that the sum of the numbers is 3?

  1. A1/12
  2. B1/36
  3. C1/6
  4. D1/18
Show answer
Answer: (D) 1/18 There are 2 favourable outcomes out of 36, so P = 1/18.
Question 7

Two fair dice are thrown. What is the probability that the sum of the numbers is 8?

  1. A5/36
  2. B5/12
  3. C1/9
  4. D1/6
Show answer
Answer: (A) 5/36 There are 5 favourable outcomes out of 36, so P = 5/36.
Question 8

Two fair dice are thrown. What is the probability that the sum of the numbers is 4?

  1. A1/6
  2. B1/4
  3. C1/12
  4. D1/9
Show answer
Answer: (C) 1/12 There are 3 favourable outcomes out of 36, so P = 1/12.
Question 9

Two fair dice are thrown. What is the probability that the sum of the numbers is 10?

  1. A1/12
  2. B1/6
  3. C1/4
  4. D1/9
Show answer
Answer: (A) 1/12 There are 3 favourable outcomes out of 36, so P = 1/12.
Question 10

Two fair dice are thrown. What is the probability that the sum of the numbers is 11?

  1. A1/18
  2. B1/12
  3. C1/36
  4. D1/6
Show answer
Answer: (A) 1/18 There are 2 favourable outcomes out of 36, so P = 1/18.

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Question 11

Two fair dice are thrown. What is the probability that the sum of the numbers is 6?

  1. A1/9
  2. B1/6
  3. C5/12
  4. D5/36
Show answer
Answer: (D) 5/36 There are 5 favourable outcomes out of 36, so P = 5/36.
Question 12

Two fair dice are thrown. What is the probability that the sum of the numbers is 7?

  1. A7/36
  2. B1/6
  3. C1/2
  4. D5/36
Show answer
Answer: (B) 1/6 There are 6 favourable outcomes out of 36, so P = 1/6.
Question 13

Two fair dice are thrown. What is the probability that the sum of the numbers is 12?

  1. A1/18
  2. B1/12
  3. C1/6
  4. D1/36
Show answer
Answer: (D) 1/36 There are 1 favourable outcomes out of 36, so P = 1/36.
Question 14

Two fair dice are thrown. What is the probability that the sum of the numbers is 12?

  1. A1/18
  2. B1/6
  3. C1/36
  4. D1/12
Show answer
Answer: (C) 1/36 There are 1 favourable outcomes out of 36, so P = 1/36.
Question 15

Two fair dice are thrown. What is the probability that the sum of the numbers is 10?

  1. A1/4
  2. B1/12
  3. C1/18
  4. D1/6
Show answer
Answer: (B) 1/12 There are 3 favourable outcomes out of 36, so P = 1/12.
Question 16

Two fair dice are thrown. What is the probability that the sum of the numbers is 8?

  1. A1/6
  2. B5/36
  3. C1/9
  4. D5/12
Show answer
Answer: (B) 5/36 There are 5 favourable outcomes out of 36, so P = 5/36.
Question 17

Two fair dice are thrown. What is the probability that the sum of the numbers is 3?

  1. A1/12
  2. B1/6
  3. C1/18
  4. D1/36
Show answer
Answer: (C) 1/18 There are 2 favourable outcomes out of 36, so P = 1/18.
Question 18

Two fair dice are thrown. What is the probability that the sum of the numbers is 9?

  1. A1/3
  2. B1/12
  3. C1/9
  4. D5/36
Show answer
Answer: (C) 1/9 There are 4 favourable outcomes out of 36, so P = 1/9.

These are RankerClub practice questions written in the GATE pattern. They are not official SSC/IBPS/RRB papers.

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