Question

If two events A and B are such that P(A∩B) = 0.4 and P(B) = 0.5, what is P(A|B)?

• A. 0.6
• B. 0.4
• C. 0.5
• D. 0.8

Answer 1

Answer: (D)

0.8

Answer 2

The problem asks us to find the conditional probability P(A|B) given P(A∩B) and P(B).

The formula for conditional probability P(A|B) is:

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

Given values:

$P(A \cap B) = 0.4$

$P(B) = 0.5$

Substitute these values into the formula:

$P(A|B) = \frac{0.4}{0.5}$

Calculate the value:

$P(A|B) = \frac{4}{5} = 0.8$

Comparing this result with the given options, the calculated value 0.8 matches the fourth option.

Use the definition of conditional probability: $P(A|B) = \frac{P(A \cap B)}{P(B)}$. Substitute the given values $P(A \cap B) = 0.4$ and $P(B) = 0.5$ into the formula. Calculate $\frac{0.4}{0.5} = 0.8$.