Question

Given that events A and B are independent with P, left parenthesis, A, right parenthesis, equals, 0, point, 1, 5P(A)=0.15 and P, left parenthesis, A, intersection, B, right parenthesis, equals, 0, point, 0, 9, 6P(A∩B)=0.096, determine the value of P, left parenthesis, B, right parenthesisP(B), rounding to the nearest thousandth, if necessary

Answer 1

To find \( P(B) \), we can use the fact that events A and B are independent. When two events are independent, the probability of their intersection is given by:

\[
P(A \cap B) = P(A) \cdot P(B)
\]

We are given:

- \( P(A) = 0.15 \)
- \( P(A \cap B) = 0.096 \)

Using the formula for the intersection of independent events:

\[
P(A \cap B) = P(A) \cdot P(B)
\]

Substituting the values we have:

\[
0.096 = 0.15 \cdot P(B)
\]

To find \( P(B) \), we can rearrange the equation:

\[
P(B) = \frac{0.096}{0.15}
\]

Now, let's calculate that:

\[
P(B) = \frac{0.096}{0.15} = 0.64
\]

Thus, the value of \( P(B) \) is:

\[
\boxed{0.640}
\]

rounded to the nearest thousandth.