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If two events Aa n dB are such that P...

If two events `Aa n dB` are such that `P(A^o)=0. 3 ,P(B)=0. 4 ,a n dP(AnnB^o)=0. 5` , then find the value of `P[B//(AuuB^o)]dot`

Text Solution

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`P(B//A(A uuB'))=(P(Bnn(AuuB')))/(P(AuuB'))`
`=(P[(BnnA)uu(BnnB')])/(P(A)+P(B)-P(AnnB'))`
`=(P(AnnB))/(P(A)P(B')-P(AnnB'))`
Now, `P(A'nnB')=0.5`
`therefore1-P(AuuB)=0.5`
`impliesP(AuuB)=0.5`
`impliesP(A)+P(B)-P(AnnB)=0.5`
`impliesP(AnnB)=0.3+0.4--0.5=0.2`
`P(AnnB')=P(A)-P(AnnB)=0.3-0.2=0.1`
`P(B//(AuuB'))=(0.2)/(0.3+0.6-0.1)=(0.2)/(0.8)=1/4`
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