A person is known to tell the truth 3 times out of 4. He tosses a dice and tells that the number coming on it is 6. Find the probability that the number coming on the dice is actually 6.

Options

A. `(3)/(8)`
B. `(1)/(5)`
C. `(3)/(4)`
D. None of these

Answer

A

Explanation

Let E denotes the event that a six occurs and A the event that the man reports that it is a 6.
Then, `P(E )=(1)/(6), P(E')=(5)/(6)`
`P((A)/(E ))=(3)/(4)` and `P((A)/(E'))=(1)/(4)`
From Baye's theorem,
`P((E )/(A))=(P(E ).P((A)/(E )))/(P(E ).P((A)/(E ))+P(E').P((A)/(E')))`
`=((1)/(6)xx(3)/(4))/((1)/(6)xx(3)/(4)+(5)/(6)xx(1)/(4))=(3)/(8)`