Question

Let A and B be events with P(A) = 0.61 and P(A ∩ B) = 0.39. For what value of P(B) will A and B be independent?

Answer 1

Answer:

$P(B) = 0.64$

Explanation:

Given

$P(A) = 0.61$

$P(A\ n\ B) = 0.39$

Required

Determine P(B)

If A and B are independent, then:

$P(A\ n\ B) = P(A) * P(B)$

Substitute values for P(A) and P(A n B)

$0.39 = 0.61 * P(B)$

Make P(B) the subject

$P(B) = \frac{0.39}{0.61}$

$P(B) = 0.64$ --- approximated