Question

A interesting question from probability.

Q . A man is known to speak the truth 3 out of 4 times . He thrown a die and reports that it is a six . find the probability that is actual a six . ​

Answer 1

Solution:-

Let E be the event that the man reports that 6 occurs, and S2 be the event that 6 doesn't occurs

P(S1) = 1/6 : P(S2) = 5/5

P(E/S1) = 3/4 , P(E/S2) = 1 - 3/4 = 1/4

By Bayes theorem :-

P(S1/E) = P(S1) P(E/S2) /P(S1) *P(E/S1) + P(S2) P(E/S2)

=> 1/6*3/4 /1/6*3/4+5/6*1/4

=> 1*3/1*3+5*1 = 3/8 Answer

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Answer 2

Step-by-step explanation:

refer to this attachment ✅✅