Consider three identical looking coins Two of the coins are

Consider three identical- looking coins. Two of the coins are ordinary fair coins (H and T are equally likely to occur on any toss) , but the third coin is 2-headed (both sides of the coin show H) . Fran and Ron each chooses a coin at
random, and the remaining coin is discarded. Suppose that Fran tosses her coin twice and Ron tosses his coin twice .

3 . Find the probability that Fran gets HH on her two tosses.
4 . Find the probability that Fran gets H on her third toss if she got HH on her first two tosses.
6 . Find the probability that Fran gets HH on her two tosses if Ron got TT on his two tosses.

Solution

3)   1/3 * (1*1 ) +2/3 * (1/2*1/2) = 1/3 + 1/6 = 1/2

4)   1/3 * (1) + 2/3 (1/8) = 1/3 + 1/12 = 5/12

5)   1/2 * (1*1 ) +1/2 * (1/2*1/2) = 1/2 + 1/8 = 5/8