Question

what is the probability that both events b and c will occur? start by finding the probability of event b. p(b) = ?/4

Explanation:

Step1: Identify probability of B

From the tree - diagram, the probability of event B is given directly as $\frac{3}{4}$.

Step2: Identify probability of C given B

The probability of C given that B has occurred is $\frac{3}{5}$.

Step3: Use multiplication rule for joint probability

The probability that both B and C occur is $P(B\cap C)=P(B)\times P(C|B)$. Substitute $P(B)=\frac{3}{4}$ and $P(C|B)=\frac{3}{5}$ into the formula. So $P(B\cap C)=\frac{3}{4}\times\frac{3}{5}=\frac{9}{20}$.

Answer:

$\frac{9}{20}$