Probability of an event is p, average attempt until p happens?

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SUMMARY

The discussion centers on the geometric distribution, which models the number of attempts required for a specific event to occur, given a probability p of that event happening in each attempt. In the example provided, a racquetball player has a 20% chance (p = 0.2) of hitting a killshot per shot. The average number of attempts until the player successfully hits a killshot can be calculated using the formula for the expected value of a geometric distribution, which is 1/p. Therefore, for p = 0.2, the average number of attempts is 5.

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Say there is a chance p of an event happening each attempt. How many attempts (on average) would it take for this event to occur once?

For example, say the event is a racquetball player hitting a killshot, which he has a 20% chance of doing every shot.

On average, how many shots until he hits a killshot? I remember learning this, but forgot the name.
 
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