Coin Probability

Question

Part a)

Suppose three coins are in a box: (1) A fair coin, (2) A coin weighted to come up heads 1/5 of the time (and tails 4/5 of the time), and (3) A two-headed coin.

A coin is drawn at random, flipped, and shows heads. What is the probability that this is the fair coin?

Part b)

Now suppose that we flip the coin again, and again we get heads. What is the probability, given that we got two heads in a row, that the coin is the fair coin?

Answer 1

Use Baye's Theorem

Part a)

P(F/H)P(H) = P(H/F)P(F)

P(F/H) = (1/2)(1/3)/17/30

= (1/6)((30/17)

= 5/17 = about 29.4% chance it's a fair coin

part b)

P(F/2H) = P(2H/F)P(F)/P(2H)

= (1/4)(1/3)/(126/300)

= about 19.8%

with 2 heads, odds are increasing it's a 2 headed coin