Multiple choice

A die is rolled. If the outcome is an odd number, what is the probability that it is prime?

  1. $\cfrac{2}{3}$
  2. $\cfrac{3}{4}$
  3. $\cfrac{5}{12}$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The odd numbers on a die are {1, 3, 5}. Among these, only {3, 5} are prime numbers. Thus, the probability is 2/3.

AI explanation

Using the conditional probability formula, we divide the probability of the intersection of the events by the probability of the given condition. The given condition is rolling an odd number, which has 3 outcomes, giving a probability of 3/6 or 1/2. The odd prime numbers on a die are 3 and 5, meaning there are 2 favorable outcomes, making the probability 2/6 or 1/3. Dividing 1/3 by 1/2 gives 2/3.

Keep practicing — related questions