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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)
P(A∩B/AUB)= ( P(A∩B)∩(AUB))/ P(AUB)
P(A∩B)∩(AUB) =P(A∩B)
P(A∩B/AUB)= P(A∩B)/ P(AUB)
P(A∩B/AUB)= 20/37
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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,
For the Next one,
That solves the two parts.
Hope that helps.
Best Regards,
Ashwin (IIT Madras).
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