Question

Two events, A and B, are associated with the following probabilities:

P(A)=23

P(A∩B)=29

If the events are independent, what is the probability of B?

P(B)= __[blank]__

Enter your answer as the fraction that correctly fills in the blank, using the / symbol, like this: 42/53

Answer 1

If A and B are independent, then
`P(A\cap B)=P(A)\cdot P(B)`.

We have:

`P(A)=(2)/(3),\ P(A\cap B)=(2)/(9)`

Substitute:

`(2)/(9)=(2)/(3)P(B)\qquad|\cdot3\\\\(2)/(3)=2P(B)\qquad|:2\\\\(1)/(3)=P(B)\\\\\boxed{P(B)=(1)/(3)}`