Question

events a and b are independent. find the indicated probability. p(a) = p(b) = 0.8 p(a and b) = 0.32

Explanation:

Step1: Recall the formula for independent events

For independent events $A$ and $B$, $P(A\text{ and }B)=P(A)\times P(B)$.

Step2: Solve for $P(A)$

We know $P(A\text{ and }B) = 0.32$ and $P(B)=0.8$. Rearranging the formula $P(A)=\frac{P(A\text{ and }B)}{P(B)}$.
Substitute the given values: $P(A)=\frac{0.32}{0.8}$.
$P(A)=0.4$

Answer:

$0.4$