Question

14) For two events, \( A \) and \( B, P(A)=.4, P(B)=.7 \), and \( P(A \cap B)=2 \). Find \( P(A \mid B) \). A). 14 B) \( .5 \) (C) 08 D) \( .25 \)

Answer 1

The probability
`\( P(A \mid B) \)` is
`\( 0.2857 \)`, which is approximately
`\( .29 \)`.

Step-by-step explanation:

Conditional probability,
`\( P(A \mid B) \)`, represents the probability of event
`\( A \)`occurring given that event
`\( B \)` has occurred. It is calculated using the formula
`\( P(A \mid B) = (P(A \cap B))/(P(B)) \).`

In this scenario,
`\( P(A \cap B) = 0.2 \) and \( P(B) = 0.7 \)`. Applying the formula,
`\( P(A \mid B) = (0.2)/(0.7) \)`, which equals approximately
`\( 0.2857 \) or \( .29 \).`

In summary, the correct answer is not provided among the given options.