# A fair coin is flipped three times. Let S be the sample space of the eight possible outcomes, and let X be the random variable that assigns to an outcome the number of heads in this outcome. What is the expected value of X?

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Answer: we already have the possible outcomes given to us as 8. And we the formula for finding the possible outcomes, is 2^n (with “n” being the number of toss or flipped in this case) which is:  2^ (3) = 8. which gives you the 8 possible outcomes. Since the coin is flipped 3 times, would have to represent each toss, 8 times to find x the number of heads.

We could have;

HHH (All heads)

TTT (All Tails)

HHT (Two heads and a Tail)

TTH (Two Tails and a head)

THT (A tail first, head then a tail again)

HTH (A head, a tail, and a head again)

HTT (Head, and two tails)

THH (Tail and two Heads)

Number of possible heads = 12

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