2. QUESTION:
A fair coin is tossed, and a fair die is thrown. Write down sample spaces for
(a) the toss of the coin;
(b) the throw of the die;
(c) the combination of these experiments.
Let A be the event that a head is tossed, and B be the event that an odd number is thrown. Directly from the sample space, calculate P(A ∩ B) and P(A ∪ B).
(a)
(b)
(c)
Clearly . We can assume that the two events are independent, so . Alternatively, we can examine the sample space above and deduce that three of the twelve equally likely events comprise . Also, , where this probability can also be determined by noticing from the sample space that nine of twelve equally likely events comprise .
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