Question

Let A and B be events with P(A) = 0.7 and P(A ∩ B) = 0.3. For what value of P(B) will A and B be independent?

Answer 1

The value of P(B) for independent events = 0.429

Explanation:

Given;

P(A) = 0.7

P(A ∩ B) = 0.3

A and B will be independent if event A will occur and B will also occur, ie A and B will occur independently.

P(A) and P(B) = P(A ∩ B)

`P(B) = ( P(A\ n\ B) )/(P(A))\\\\ P(B) = (0.3)/(0.7)\\\\P(B) = 0.429`

Therefore, the value of P(B) for independent events = 0.429