A man speaks the truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even. The probability that it is actually even is

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Concept:

E = the event a man reports that it is even

E= the event of an even number is picked

E= the event of an odd number is picked

To find : The probability that it is actually even i.e. P(E1|E)

P(E1|E) = 

 

Calculations:

Given, a man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even.

E= the event of an even number is picked

E= the event of an odd number is picked

⇒P(E1) = 

⇒P(E2) = 

E = the event a man reports that it is even

 A man speaks truth 2 out of 3 times.

⇒P(E|E1) = 

⇒P(E|E2) = 

To find : The probability that it is actually even i.e. P(E1|E)

P(E1|E) = 

⇒P(E1|E) = 

⇒P(E1|E) = 

⇒⇒P(E1|E) = 

Hence, a man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even. The probability that it is actually even is 

 

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