rolling dice probability

Question

Suppose a single fair die is rolled. Find the probability that it is a 4​, given that it is an odd number.

Answer 1

The question is asking for a conditional probability.

The formula for conditional probability is P(A|B) = P(A intersect B) divided by P(B).

Here, we'll let A = event that a 4 is rolled. Set A = {4}.

and we'll let B = event that an odd number is rolled. Set B = {1, 3, 5}.

Given sets A and B, the intersection set of A and B is the empty set.

We also need the sample space which is the set {1, 2, 3, 4, 5, 6} or the set of all possible outcomes when rolling a die.

As such, the P(A intersect B) = (number of items in set A intersect B) divided by (number of items in sample space) = 0/6 = 0.

The P(B) = (number of items in set B) divided by (number of items in sample space) = 1/6.

Hence, the P(A|B) = 0 divided by 1/6 = 0.