Multiple choice

A symmetrical die is rolled. If an odd number comes up on it, then the probability of getting a prime number greater than $3$ on it is

  1. $\dfrac{1}{2}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{1}{4}$
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B Correct answer
Explanation

Odd numbers on a die are {1, 3, 5}. Prime numbers on a die are {2, 3, 5}. Prime numbers greater than 3 are {5}. Given that an odd number came up, the sample space is {1, 3, 5}. Only {5} is a prime number greater than 3. Thus, the probability is 1/3.

AI explanation

The problem uses conditional probability, defined as the probability of event A given event B, calculated as the probability of A and B divided by the probability of B. The odd numbers on a die are 1, 3, and 5, making the sample space for the condition exactly 3 outcomes. The only odd prime number greater than 3 is 5, giving 1 favorable outcome, so the conditional probability is 1 divided by 3.

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