With their soccer match tied, Emek and Tara studied the records for their team's next penalty kicker. In recent practice, the kicker had scored 18 of 24 attempts aimed left, 14 of 20 aimed center, and 21 of 28 aimed right. The opposing goalkeeper's record showed that in 40 penalty kicks, the goalkeeper had dived left 18 times, stayed in the center 8 times, and dived right 14 times. Emek calculated the kicker's scoring rates: 75% left, 70% center, and 75% right. Since left and right had equal scoring rates, Tara compared the goalkeeper's behavior. The goalkeeper chose left 45% of the time but right only 35% of the time. Based on those records, they recommended aiming right because it combined one of the kicker's highest scoring rates with the direction the goalkeeper chose less often. The kicker followed their plan and scored. As the team celebrated, Emek and Tara knew the data had helped them make a better-informed decision.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Compare the percentages scored in each direction.
Based on the kicker's practice record, which direction had the lowest scoring rate?
LeftCenterRightLeft and right equally
Correct. The center scoring rate was 70%, lower than the 75% rates for left and right.
Compare 18 out of 24, 14 out of 20, and 21 out of 28 as percentages.
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Hint
Subtract the number of right dives from the number of left dives.
In the goalkeeper's record of 40 penalty kicks, how many more times did the goalkeeper dive left than dive right?
Correct. The goalkeeper dived left 4 more times than right.
Use the recorded counts of 18 left dives and 14 right dives.
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Hint
For each direction, first find the probability that the goalkeeper does not choose it, then multiply by the kicker's scoring rate.
Suppose Emek estimates the chance of scoring in a direction by multiplying the kicker's scoring rate by the probability that the goalkeeper does not choose that same direction. Using the story data, which direction gives the greatest estimated chance?
Left, because 0.75 x 0.55 = 0.4125Center, because 0.70 x 0.80 = 0.56Right, because 0.75 x 0.65 = 0.4875Left and right, because both have a 75% scoring rate
Correct. Under this simplified estimate, center gives the largest product, 0.56.
Calculate all three products. The goalkeeper's center frequency is 8 out of 40, so the probability of not choosing center is 0.80.
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Penaltı Kararı
TR
ARC_G09_DP_02_STORY_01
Penaltı Kararı
The Penalty Kick Decision
EN
ARC_G09_DP_02_STORY_01
The Penalty Kick Decision