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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, June 2018

2018-06-25

Penalty Shoot-Out

Goal Gate
Find out the probability that player B will win!

Two soccer players compete in a penalty shoot-out. Player A scores every other shot, and player B scores every third shot. They take turns shooting until one of them scores a goal.

What is the probability that player B will win, if he goes first?


Solution

The probability that B will win is 50%. You can see this in the following diagram. There are three possibilities per round:

  • B scores
  • B misses
  • neither of them scores a goal (standoff)

Every result has a probability of 1/3. If the match ends in a standoff, it starts over with the same probabilities for the three possible results.


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