Before a soccer tournament, Tara and Emek studied 60 penalty kicks taken by their upcoming opponent. They organized the records in a table by direction and outcome. Of 24 kicks aimed left, 18 scored. Of 20 aimed toward the center, 13 scored. Of 16 aimed right, 10 scored. Tara calculated the conditional scoring probabilities for each direction: 18/24 = 0.75 for left, 13/20 = 0.65 for center, and 10/16 = 0.625 for right. Emek noted that simply comparing the numbers of goals could be misleading because the opponent had not attempted the same number of kicks in each direction. The conditional probabilities showed that kicks to the left presented the greatest scoring risk. Overall, the opponent had scored 41 of 60 penalties, about 68.3%, but the left-side rate was noticeably higher. Based on the model, Tara and Emek recommended that the goalkeeper pay particular attention to signs that a kicker was preparing to aim left. Their analysis gave the team a focused defensive strategy for the tournament.

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Because the kick is known to have been aimed right, use only the right-side kicks as the relevant group.
Which probability best represents the chance that a penalty kick scored, given that it was aimed to the right?
10/6016/6010/1641/60
Correct. Of the 16 kicks aimed right, 10 scored, so the conditional probability is 10/16.
Not quite. For a conditional probability given that the kick went right, the denominator should be the total number of right-side kicks.
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Hint
Use the total number of kicks and the total number that scored.
Among the 60 penalty kicks in the study, how many kicks did not result in a goal?
Correct. There were 19 penalties that did not result in goals.
Check the difference between the 60 total kicks and the 41 that scored.
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Hint
The opponent attempted 24 kicks left, 20 center, and 16 right, so the group sizes are different.
Why is comparing the conditional scoring rates more informative than comparing only the numbers of goals scored in each direction?
Conditional rates account for the different numbers of attempts in each direction.Conditional rates guarantee that the direction with the most attempts has the highest scoring probability.Conditional rates ignore unsuccessful kicks and use only goals.Conditional rates make all three directions have the same number of attempts.
Correct. Conditional probabilities compare scoring success relative to the number of attempts in each direction.
Not quite. Think about why raw goal totals can be misleading when the numbers of attempts are unequal.
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Penaltı Vuruşunu Okumak
TR
ARC_G12_DP_02_STORY_02
Penaltı Vuruşunu Okumak
Reading the Penalty Kick
EN
ARC_G12_DP_02_STORY_02
Reading the Penalty Kick