If A and B are two independent events such that P (A) =`1//2, P(B)=1//5,` then find `P(AuuB) and `P(A|B)

Options

A. `P(AuuB)=3//5`
B. `P(A|B)=1//4`
C. `P(A//AuuB)=5//6`
D. `P(AnnB\|barAuubarB)=0`

Answer

A, C, D

Explanation

Since A and B are independent events, we have
`P(AnnB)=P(A)P(B)=1/2xx1/5=1/10`
`P(A//B)=P(A)=1/2`
Now, `P(AuuB)P(A)+P(B)-P(AnnB)`
`=1/2+1/5-1/10=3/5`
Now, `P(A//AuuB)=(P[Ann(AuuB)])/(P(AuuB))=(P(A))/(P(AuuB))=(1//2)/(3//5)=5/6`
`P[(AnnB)//(barAuubarB)]=P(AnnB//(bar(AnnB)))=0`