A speaks the truth 8 times out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

is it the questn of total probabilty , or bayes theorem . identify kaise krna h isko experts .

shukria .

Let E_{1} : The event that 5 comes on the die

and E_{2 }: The event that 5 does not comes on the die

A: The event that man report it is a five

Probability that the man reports that there is a five on the die given than five comes on the die

Probability that the man reports that there is a five on the die given that five does not comes on the die

∴ By Baye's Theorem,

We have Probability that there is a five given than man reports that there is a five on the die

The questions in which we have any event say A which occurs with E_{1} or E_{2} or ..... or E_{n} , then we apply Baye's Theorem to find the Probability of E_{i} when A has already happened i.e. to find

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