Question

Let A and B be two events. Suppose that P(A)=0.60

and P(B)=0.39.

(a) Find P(AorB), given that A and B are independent.

(b) Find P(AorB), given that A and B are mutually exclusive.

Answer 1

`\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)`

Because
`A` and
`B` are independent, you have
`\mathbb P(A\cap B)=\mathbb P(A)*\mathbb P(B)`, so


`\mathbb P(A\cup B)=0.60+0.39-0.60*0.39=0.756`

If
`A` and
`B` are mutually exclusive, you have


`\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)=0.60+0.39=0.99`