Coin flips
Probability
Level
pending
Max flips a coin 10 times in a row. Assuming that the coin is fair, what is the probability of Max flipping more heads than tails? (give your answer as a decimal rounded to the nearest hundredth)
The answer is 0.38.
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1 solution
The probability of Max flipping more heads than tails and the probability of him flipping more tails than heads is equal. However, the probability of Max flipping an equal number of heads and tails needs to be taken into account: There are 10 coin flips, so that gives (1/2)^10, but then there are 10C5 (10 choose 5) ways to order the five heads and the five tails, so that probability would be (1/2)^10 x 10C5 = 63/256. What we want is the probability that Max flips more heads than tails, which would be (1 - (probability of equal heads and tails))/2, since more heads than tails is the same as more tails than heads. Thus, the desired probability is (1 - 63/256)/2 = 193/512 = .37695.... which rounds to .38.