If A and B are two events such that `P(A)=1/2, P(AuuB)=3/5` and `P(B)=p`, then find the value of `p` when:
(i) A and B are mutually exclusive
(ii) A and B are independent events.

Explanation

`P(A)=1 / 2, P(B)=p`

`
P(AUB)=3 / 5`


i) Mutually exclusive `P(A cap B)=0`

`
P(A U B)=P(A)+P(B)-P(A cap B)`

`
3 / 5=1 / 2+{p}-{O}`

`
p=1 / 10`


ii)Independent events `P(A cap B)=P(A)^{*} P(B)=p / 2`

`
P(AUB)=P(A)+P(B)-P(A cap B)`

`
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