Mildred Smith has a friend who claims she can tell whether cream is added to coffee before or after the coffee is poured. Mildred’s prior belief of her friend’s claim is 20%. That is, she believes...

Mildred Smith has a friend who claims she can tell whether cream is added to coffee before or after the coffee is poured. Mildred’s prior belief of her friend’s claim is 20%. That is, she believes that the probability her friend’s claim is true is .20. Mildred decides to test her friend’s claim by making 10 cups of coffee and not showing her friend how the coffee was prepared. To prepare the coffee, she flips a coin. If the coin comes up heads she adds cream to the coffee, and if the coin comes up tails she adds coffee to the cream. Mildred’s friend correctly identifies how the coffee was made in each of the 10 cases. What should Mildred’s posterior belief be regarding her friend’s claim?