Two dice are thrown. What is the probability that the sum of numbers on the dice is a prime number?

Question

Question

This question was previously asked in

OSSC CGL Official Paper 2023 (Held on 14th May 2023)

Answer 1

Given Data:

Number of outcomes when two dice are thrown: 6 × 6 = 36.

Concept:

The probability of an event is determined by dividing the number of favourable outcomes by the total number of outcomes.

Solution:

⇒ Possible prime sums when two dice are rolled are 2, 3, 5, 7, 11. We determine the ways to achieve these prime numbers.

⇒ The summation 2 can result from the pair (1, 1). This gives us 1 way.

⇒ The summation 3 can result from the pairs (1, 2), (2, 1). This gives us 2 ways.

⇒ The summation 5 can result from the pairs (1, 4), (4, 1), (2, 3), (3, 2). This gives us 4 ways.

⇒ The summation 7 can result from the pairs (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3). This gives us 6 ways.

⇒ The summation 11 can result from the pairs (5, 6), (6, 5). This gives us 2 ways.

⇒ Total favourable outcomes = 1 + 2 + 4 + 6 + 2 = 15.

⇒ Probability is calculated by dividing the favourable outcomes by the total outcomes.

⇒ Probability = Favourable outcomes / Total outcomes = 15 / 36 ⇒ 5/12

Hence, the correct answer is 5/12.

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