There are 11 players in team A. It is known that four of them (call them high scoring) score a penalty with probability 0.8 each and the other seven (

facas9

facas9

Answered question

2020-11-22

There are 11 players in team A. It is known that four of them (call them high scoring) score a penalty with probability 0.8 each and the other seven (low-scoring) with probability 0.5 each.
There is a penalty shoot-out with another team, team B (of 11 players), in which every player from each team takes exactly one shot, so that 22 shots are to be taken. Every player in team B scores with probability 0.64. The team that scores the most goals wins. Which team is expected to win? Justify your answer

Answer & Explanation

cheekabooy

cheekabooy

Skilled2020-11-23Added 83 answers

Every player in team B scores with probability 0.64 so the expected value of scoring of team B is: (11)(0.64)=7.04.
The expected value of scoring of team A is: (4)(0.8)+(7)(0.5)=6.7.
So, without rounding, 7.04>6.7 which means that the expected value of scoring of team B is greater than the expected value of scoring of team A, So team B is expected to win.
But if you take the round of the two values, 7.04 and 6.7, to the nearest integer, the two results are equal to 7 which means that the two teams are tied (draw or equality).

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