if `A` and `B` be two events such that `P(A)=1/4, P(B)=1/3` and `P(AuuB)=1/2,` show that `A` and `B` are independent events.

Explanation

For independent events `A` and `B`, `P(AnnB) = P(A)P(B)`.

Also, `P(AuuB) = P(A)+P(B)-P(AnnB)`

Putting the given values,

`1/2 = 1/4+1/3 -P(AnnB)`

`1/2 = 7/12 - P(AnnB)`

`=>P(AnnB) = 7/12 - 1/2 = 1/12`

`=>P(AnnB) = 1/4**1/3 = P(A)P(B)`

Thus, `A` and `B` are independent events.