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Question

# Mohan posts a letter to Sohan. It is known that one letter out of 10 letters does not reach its destination. It is certain that Sohan will reply if he receives the letter. If A denotes the event that Sohan receives the letter and B denotes the event that Mohan gets a reply, then

A
P(B)=81100
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B
P(AB)=81100
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C
P(A|¯¯¯¯B)=919
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D
P(AB)=910
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Solution

## The correct options are A P(B)=81100 B P(A∩B)=81100 C P(A|¯¯¯¯B)=919 D P(A∪B)=910A: Sohan receives the letter. B: Mohan gets a reply. P(B)=P( Sohan receives the letter)× P (Sohan writes a reply)× P( Mohan gets the letter) =910×1×910=81100 P(A∩B)=P(B)=81100 P(A|¯¯¯¯B)=P(A∩¯¯¯¯B)P(¯¯¯¯B) P(¯¯¯¯B)=1−P(B)=19100⇒P(A∩¯¯¯¯B)=910×1×110⇒P(A|¯¯¯¯B)=919 P(A∪B)=P(A)+P(B)−P(A∩B) ⇒P(A∪B)=910+81100−81100 ⇒P(A)=910

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