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

Answer:

Step-by-step 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

$P(B1) = \frac{1}{3} \\ P(B2) \frac{2}{3}$

P(AB1) = $\frac{1}{2} *\frac{1}{3} =\frac{1}{6}$

P(AB2) = $\frac{2}{3} \frac{1}{2} =\frac{2}{6}$

Required probability = P(B1/A)=$\frac{P(B1A)}{P(B1A)+P(B2A)} \\=\frac{\frac{1}{6} }{\frac{1}{6}+\frac{2}{6}} \\=\frac{1}{3}$