Given that events $\mathrm{A}$ and $\mathrm{B}$ are independent with $P(A)=0.32$ and $P(B)=0.95$, determine the value of $P(A \cap B)$, rounding to the nearest thousandth, if necessary.
Answer
\(\boxed{0.304}\)
Step 1 ：Given that events \(A\) and \(B\) are independent with \(P(A)=0.32\) and \(P(B)=0.95\), determine the value of \(P(A \cap B)\), rounding to the nearest thousandth, if necessary.
Step 2 ：Since events A and B are independent, we can use the formula for the probability of the intersection of two independent events: \(P(A \cap B) = P(A) * P(B)\). We are given \(P(A) = 0.32\) and \(P(B) = 0.95\). We can plug these values into the formula and calculate the result.
Step 3 ：\(P(A \cap B) = P(A) * P(B) = 0.32 * 0.95 = 0.304\)
Step 4 ：\(\boxed{0.304}\)
