Question

You randomly draw a coin from 100 coins — 1 unfair coin (head-head), 99 fair coins (head-tail) and roll it 10 times. If the result is 10 heads, what is the probability that the coin is unfair?

Answer 1

This can be answered using the Bayes Theorem. The extended equation for the Bayes Theorem is the following:

Assume that the probability of picking the unfair coin is denoted as P(A) and the probability of flipping 10 heads in a row is denoted as P(B). Then P(B|A) is equal to 1, P(B|¬A) is equal to 0.5¹°, and P(¬A) is equal to 0.99.

If you fill in the equation, then P(A|B) = 0.9118 or 91.18%.