If A and B are two independent events such that `P(A)=(1)/(2)` and `P(B)=(1)/(5)` then which of the following is correct ?

Options

A. `P(A cup B)=3//5`
B. `P(A//B)=1//2`
C. `P(A//A cup B)=5//6`
D. `P(A cap B//overline(A) cup overline(B))=1//2`

Answer

D

Explanation

Since A and B are independent events. Therefore,
`P(A cap B)=P(A)P(B)=(1)/(2)xx(1)/(5)=(1)/(10)`
and, `P(A//B)=P(A)=(1)/(2)`
So, alternative (b) is correct.
Now,
`P(A cup B)=P(A)+P(B)-P(A cap B)=(1)/(2)+(1)/(5)-(1)/(10)=(3)/(5)`
So, alternative (a) is correct.
Now,
`P(A//A cup B)=(P[A cap (A cup B)])/(P(A cup B))=(P(A))/(P(A cup B))=(1//2)/(3//5)=(5)/(6)`
So, alternative (c ) is correct.
and, `P(A cap B//overline(A) cup overline(B))=P(overline(A cup B))=0`