If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________

Category: QuestionsIf P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________
Editor">Editor Staff asked 11 months ago

If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________
 
(a) 3/5
 
(b) 2/3
 
(c) 1/2
 
(d) 1
 
I had been asked this question in an international level competition.
 
The question is from Conditional Probability in chapter Probability of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right option is (d) 1
 
Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
 
Also P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)
 

8/11 = 7/11 + 6/11 – P(A∩B)
 

P(A∩B) = 13/11 – 7/11
 

P(A∩B) = 6/11
 
P(A|B) = (6/11) / (6/11).
 
P(A|B) = 1.