Given that P(A and B) = 0.20 and P(A|B) = 0.40, what must the P(B) =

Question

Question 7 options:

0.1

0.5

0.2

0.4

Answer 1

We can use the formula for conditional probability to find \( P(B) \). The formula is:

\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]

We know:

• \( P(A \text{ and } B) = 0.20 \)
• \( P(A|B) = 0.40 \)

Substituting these values into the conditional probability formula:

\[ 0.40 = \frac{0.20}{P(B)} \]

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

\[ P(B) = \frac{0.20}{0.40} \]

Calculating this gives:

\[ P(B) = 0.50 \]

Thus, the correct option is:

0.5