Question

A group of 10 students participate in chess club, karate club, or neither.

Answer 1

Answer: Option B

$P(A|B)=0.50$

Step-by-step explanation:

We look for the conditional probability of A given B.

This is written as:

$P(A|B) = \frac{P(A\ and\ B)}{P(B)}$

First we must find the probability of A and B

There are 10 students in total. Note that of those 10 students only 2 of them are at the same time in the karate club and in the chess club

Therefore:

$P(A\ and\ B)=\frac{2}{10}$

There are 10 students in total. Note that of those 10 students only 4 of them are in the chess club

Then:

$P(B)=\frac{4}{10}$

Finally:

$P(A|B) = \frac{P(0.2)}{0.4}=0.50$