Given that P(A)=0.8, P(A/B)=0.8 , P(A∩B)=0.5, Find

(i)P(A/AUB) Answer-32/37

(ii)P(A∩B/AUB) Answer-20/37

Dear Shaleen,

  P(A)=0.8, P(A/B)=0.8 , P(A∩B)=0.5       Given

and we know that the conditional probability 

P(A/B)= P(A∩B)/ P(B)   so we can find  P(B)= 5/8

from this we can find  P(AUB) = P(A)+P(B)-P(A∩B)

P(AUB) = 37/40

P(A/AUB) =  P(A∩(AUB)/ P(AUB)

as     P(A∩(AUB) =P(A)    set theory 

so we get 

 P(A/AUB) = P(A)/ P(AUB)

 P(A/AUB)=(8/10)/(37/40)

 P(A/AUB)=32/37  

2)       

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jitender

askiitians expert

Hi Shaleen,

P(A)=0.8, P(A/B)=0.8 , P(A∩B)=0.5       

Now conditional Probability,

P(A/B)= P(A∩B)/ P(B)   

Hence  P(B)= 5/8

Next, P(AUB) = P(A)+P(B)-P(A∩B)

So P(AUB) = 37/40

And, P(A/AUB) =  P(A∩(AUB)/ P(AUB) -------[as P(A∩(AUB) =P(A)]

So,

 P(A/AUB) = P(A)/ P(AUB)

 P(A/AUB)=(8/10)/(37/40)

 P(A/AUB)=32/37  

 For the Next one,

That solves the two parts.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).