Question

There is a fair coin (one side heads, one side tails) and an unfair coin (both sides tails). You pick one at random, flip it 5 times, and observe that it comes up as tails all five times. What is the chance that you are flipping the unfair coin?

Answer 1

Answer:

0.9697

Step-by-step explanation:

given that there is a fair coin and an unfair coin.

(both sides tails)

Let B = all tails 5 times

A1- fair coin

A2 - unfair coin

$P(B/A1) = 0.5^5P(B/A2) = 1$

P(A1) = 0.5 and P(A2) =0.5 (since each coin is equally likely to be selected)

Required probability

= Prob (unfair coin/all tails) =P(A2/B)

= $\frac{P(A2B)}{P(A1B)+P(A2B)} \\=\frac{0.5(1}{0.5(0.5^5+1)} \\=0.9697$