You flip a coin 3 times. Each time the coin lands on heads, you roll a die and record the result. If it lands on tails you don’t roll the die and you don’t record a result. In other words, if your coin lands on heads three times and tails once, then you would roll the die 3 times. If the coin lands on heads once, then you would only roll the die once. If the roll(s) of the dice (or die if it was only one) add up to the number four. Find the following:

(a) Probability that the coin landed on heads once

(b) Probability that the coin landed on heads twice

(c) Probability that the coin landed on heads three times

(d) Expected value of the number of times the coin landed on heads.

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