2. (Monty Hall) Suppose you are on a game show and are presented with three closed doors

marked door 1, 2, and 3. Behind one door is a prize and behind the other two are goats.

Suppose the host allows you to select one door, but the following two rules apply:

Before it is opened the host opens one of the two unselected doors that has a goat behind

it.

The host then allows you to switch your choice to the remaining door or stay with your

original choice.

Say you select door 1. If the host then opens door 3 to reveal a goat, compute the probability

the prize is behind door 2. , use the following events for computing:

D1 = The prize is behind door 1

D2 = The prize is behind door 2

D3 = The prize is behind door 3

H1 = the host opens door 1

H2 = the host opens door 2

H3 = the host opens door 3

In other words, compute P(D2 | H3). What would you do in this situation, stay or switch?

Hint: Use Bayes' Theorem and the Law of Total Probability