Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
9 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  



We are all IITians and here to help you in your IIT JEE preparation.

Now you can win by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..  

jitender

askiitians expert

Ashwin Muralidharan IIT Madras
290 Points
9 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).

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free