Question

Your friend tossed a fair coin when you weren’t around. She has a habit of messing with you every once in a while, and so there is a 1/3 chance that she will lie to you about the result of the coin toss (report heads as tails and tails as heads), and 2/3 chance that she will tell you the true result of the coin toss. Suppose she claims that the coin toss resulted in heads. What’s the probability that she’s lying?

Answer 1

Explanation:

Given that your friend tossed a fair coin when you weren’t around.

Let A be the event that she said the outcome is head

B1 = Event she lied and B2 = Event she did not lie

`P(B1) = (1)/(3)    \\ P(B2) (2)/(3)`

P(AB1) =
`(1)/(2) *(1)/(3) =(1)/(6)`

P(AB2) =
`(2)/(3) (1)/(2) =(2)/(6)`

Required probability = P(B1/A)=
`(P(B1A))/(P(B1A)+P(B2A)) \\=((1)/(6) )/((1)/(6)+(2)/(6)) \\=(1)/(3)`