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 not true ?

Options

A. `P(A uuB)=(3)/(5)`
B. `P((A)/(B))=(1)/(4)`
C. `P((A)/(AuuB))=(5)/(6)`
D. `P((AnnB)/(bar(A)uubar(B)))=0`

Answer

B

Explanation

Since A and B are independent events.
`P(A nnB)=P(A)P(B)=(1)/(2)xx(1)/(5)=(1)/(10) and P((A)/(B))=P(A)=(1)/(2)`
So, alternative (b) is true.
Now, `P(A uu B)=P(A)+P(B)-P(A nnB)`
`=(1)/(2)+(1)/(5)-(1)/(10)=(3)/(5)`
So, alternative (1) is true.
Now, `P((A)/(A uu B))=(P[Ann(AuuB)])/(P(AuuB))=(P(A))/(A(AuuB))=(1//2)/(3//5)=(5)/(6)`
and `P((AnnB)/(bar(A)uubar(B)))=0`
So, alternatives (C) and (D) also hold good.