# 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 E1 : The event that 5 comes on the die

and E2 : 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 E1 or E2 or ..... or En , then we apply Baye's Theorem to find the Probability of Ei when A has already happened i.e. to find

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this is bayes theorm

let E1 be the event that out come is 5

let E2 be event that outcome is not 5

let A be the event that he declared it's 5

p(E1)=1/6;p(E2)=5/6;

p(A/E1)=8/10=4/5

(p(A/E2)=1/5

now solv using bayes theorm find p(E1/A)

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