Consider an experiment in which two 6-sided die are thrown. Let E be the event "both dice are at least four."

(i) How many outcomes are in E?

(ii) Give an example of an event F such that E and F are mutually exclusive. Be sure to explain why E and F are mutually exclusive.

(iii) The first dice is fair, so that p1(x) = 1/6 for each x, but the second dice has the following probability distribution:

p2(x) = 1/4 x is even

1/12 x is odd

What is P(E)?

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