what is the probability that both events b and c will occur? start by finding the probability of event b…

Explanation:

Step1: Identify probability of B

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

Step2: Calculate P(B and C)

We use the multiplication rule for conditional probabilities. Since the probability of C given B is $\frac{3}{5}$, and $P(B)=\frac{3}{4}$, then $P(B\cap C)=P(B)\times P(C|B)$. $P(B\cap C)=\frac{3}{4}\times\frac{3}{5}=\frac{9}{20}$.

Answer:

$\frac{9}{20}$