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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

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

Grade:12

2 Answers

jitender lakhanpal
62 Points
11 years ago

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)

putting the values we get 

P(A∩B/AUB)= 20/37  



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Ashwin Muralidharan IIT Madras
290 Points
11 years ago

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,

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)

Substituting the values from above,

P(A∩B/AUB)= 20/37  

That solves the two parts.

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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