A hockey player scores by probability of 18%. How many shots does he expect to take before he can score a goal.

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A hockey player scores by probability of 18%. How many shots does he expect to take before he can score a goal.

Mathematics
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if the player makes 50% of the shots, how many would you expect him to need to shoot before he makes one?

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Geometric distribution: The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...} The expected value of N for the first success is 1/p where p=0.18 for this problem. See: https://en.wikipedia.org/wiki/Geometric_distribution
The means that if we repeat the same experiment many times, there will be an equal number of outcomes above and below N=1/p. If p=0.4, then N=1/0.4=2.5. If the same experiment is repeated say 1000 times, then \(approximately\) 500 need 3 or more tries, and 500 will need 2 or less tries.

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