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Let E1 : The event that 5 comes on the die
and E2 : The event that 5 does not comeson 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

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)
and E2 : The event that 5 does not comeson 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

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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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)