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If Aa n dB are two independent events su...

If `Aa n dB` are two independent events such that `P(A)=1//2 a n d P(B)=1//5,` then

A

`P(AuuB)=3//5`

B

`P(A|B)=1//4`

C

`P(A//AuuB)=5//6`

D

`P(AnnB\|barAuubarB)=0`

Text Solution

Verified by Experts

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`
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