Coin Flipping
Probability
Level
3
Eli flips 8 coins and Calvin flips 7. What is the probability that Eli flips more heads than Calvin?
The answer is 0.5.
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1 solution
After 7 flips each, the probability that Eli has more heads is p , which by symmetry is the same as Calvin having more heads. If Eli is ahead, he has won; if Calvin is ahead, Eli cannot win, since at best he could tie. If they are tied (with probability 1 − 2 p ), Eli needs a heads on his last flip to have more than Calvin. The total probability is p + 2 1 ( 1 − 2 p ) = 0 . 5 .