SOLUTION: There are 5 coins in a bag: 3 weighted coins with Pr[H]=8/9 and 2 fair coins. One is chosen at random and flipped 180 times. What is the expected number of H flipped?

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Question 1191469: There are 5 coins in a bag: 3 weighted coins with Pr[H]=8/9 and 2 fair coins. One is chosen at random and flipped 180 times. What is the expected number of H flipped?
Answer by greenestamps(13200) About Me  (Show Source):
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If a fair coin is chosen and flipped 180 times, the expected number of heads will be 180(1/2) = 90.

If a weighted coin is chosen and flipped 180 times, the expected number of heads will be 180(8/9) = 160.

The probability that a fair coin is selected is 2/5; the probability that a weighted coin is selected is 3/5.

The expected number of heads in the described experiment is then

(2/5)(90)+(3/5)(160) = 36+96 = 132

ANSWER: 132