Problem 2 20 points Suppose that we have a fair die and two

Problem 2: 20 points. Suppose that we have a fair die and two unbiased coins. A student throws all three objects and waits for them to land on the ground. He then records the number of the die and the head/tail?s status of the coin. Identify the possible outcomes of the student?s action and the probability of each outcome.

Solution

Possible outcomes are

{1HH},{1HT},{1TT},

{2HH},{2HT},{2TT},

{3HH},{3HT},{3TT},

{4HH},{4HT},{4TT},

{5HH},{5HT},{5TT}

{6HH},{6HT},{6TT}.

probability of outcomes of

{{1HH},{1TT},{2HH},,{2TT},{3HH},{3TT},{4HH},{4TT},{5HH},{5TT},{6HH},{6TT}} = 1/6*1/2*1/2 = 1/24 for each

and probability of outcomes for

{{1HT},{2HT},{3HT},{4HT},{5HT},{6HT}}= 1/6*2*1/2*1/2 = 1/12 for each