A person holds...

Question

A person holds a two-tailed coin in one hand and a fair coin in the other. A hand is chosen at random and the coin is flipped. If tails shows, what is the probability that it is the two-tailed coin?

Answer 1

This is a conditional probability

 

This is done best with the use of a tree diagram

 

 

Prob (2 tailed given tail) = prob (tail from 2 tailed) / prob tail

 

prob (tail from 2 tail) = 1/2 * 1  = 0.5

 

prob tail = tail from 2 tailed + tail from fair coin = 0.5  + 0.5 * 0.5 = 0.75

 

so final answer = 0.5/0.75 = 0.667

 

 

 

Hope this helps