Question
Download Solution PDFA 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
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
E = the event a man reports that it is even
E1 = the event of an even number is picked
E2 = 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.
E1 = the event of an even number is picked
E2 = 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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