Question

An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:
Event A: The outcome of the rolled die is a prime number.
Event B: The outcome of the rolled die is an odd number less than 4.
The conditional probability of A given B, denoted by P(A|B), is ______ (rounded off to one decimal place).

Hint:

List the outcomes in event B, then find what fraction of those outcomes are also prime.

Answer 1

Correct Answer: 0.5

Alternate method: reduced sample space.
Since event B has occurred, restrict attention to the reduced sample space $B = \{1, 3\}$, equally likely given that B occurred.
$1$ is not prime, $3$ is prime. Out of 2 equally likely outcomes, exactly 1 satisfies A.
\[ P(A|B) = \frac{1}{2} = 0.5 \]
This confirms $P(A|B)=0.5$.