Before a championship soccer match, Tara and Emek studied how to arrange the team's first three penalty kicks. The statistics showed that Player A scored with probability 0.90, Player B with 0.80, and Player C with 0.70. Their tree diagram showed that the probability all three would score was 0.90 times 0.80 times 0.70 = 0.504, regardless of order. However, the coaches especially wanted a strong start with both of the first two kicks scored. If A and B kicked first, that probability was 0.90 times 0.80 = 0.72. With A and C first, it was 0.63, and with B and C first, it was 0.56. Tara noted that changing the order did not change the probability of three successful kicks, but it did affect the chance of scoring both opening attempts. Emek therefore recommended A and B for the first two kicks. With the strategy decided, the team entered the match prepared for a possible shootout.

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Challenges

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Challenge 1 of 4
Hint
Compare the probabilities 0.72, 0.63, and 0.56 for the possible opening pairs.
The coaches want to maximize the probability that both of the first two penalty kicks are scored. Which pair should Tara and Emek recommend for the first two kicks?
Players A and C, because their probability of both scoring is 0.63.Players B and C, because their probability of both scoring is 0.56.Any pair, because the order does not affect the probability of the first two kicks both being scored.Players A and B, because their probability of both scoring is 0.72.
Correct! A and B give the greatest probability of scoring both opening kicks.
Not quite. Choose the pair with the greatest probability that both players score.
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Hint
Multiply the probability 0.72 by the number of situations.
If Players A and B take the first two kicks, the probability that both score is 0.72. In 100 similar shootout situations, how many times would both opening kicks be expected to be scored?
Correct! In 100 similar situations, both opening kicks would be expected to be scored 72 times.
Try again. Multiply 0.72 by 100 to find the expected number of successful opening pairs.
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Hint
For all three to score, the same three probabilities are multiplied in either order. For the first two to score, compare A and B with C and A.
The coaches consider changing the order from A-B-C to C-A-B. Which statement correctly compares the probability that all three players score with the probability that the first two players score?
The probability all three score remains 0.504, but the probability the first two score changes from 0.72 to 0.63.The probability all three score changes from 0.504 to 0.63, while the probability the first two score remains 0.72.Both probabilities remain unchanged because the same three players are taking the kicks.The probability all three score changes to 0.56, and the probability the first two score changes to 0.504.
Correct! Reordering does not change the product for all three players, but it changes which two probabilities determine a successful start.
Not quite. Separate the event that all three score from the event that only the first two score.
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Penaltı Atışlarını Planlamak
TR
ARC_G11_DP_02_STORY_02
Penaltı Atışlarını Planlamak
Planning the Penalty Shootout
EN
ARC_G11_DP_02_STORY_02
Planning the Penalty Shootout