At the track championship, Tara and Emek helped choose a pairing for the final two relay positions. Practice records showed results from 20 trials for each possible pairing. Pair A completed 16 clean baton exchanges and finished under the target time in 15 trials; both requirements were met in 13 trials. Pair B completed 18 clean exchanges and finished under the target time in 14 trials; both occurred in 12 trials. Tara calculated the combined probabilities: 13/20, or 65%, for Pair A and 12/20, or 60%, for Pair B. Emek then examined the results conditionally. Given that Pair A completed a clean exchange, it also finished under the target time in 13 of 16 trials, a probability of 81.25%. For Pair B, the corresponding probability was 12/18, or about 66.7%. Although Pair B had more clean exchanges overall, Pair A performed better when both requirements were considered. Tara and Emek recommended Pair A, and the coach used their analysis to finalize the relay order.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Because the trial is known to have finished under the target time, use the 15 such trials as the total.
For Pair A, 15 of 20 trials finished under the target time, and 13 trials had both a clean exchange and a finish under the target time. What is the probability that Pair A completed a clean exchange given that it finished under the target time?
13/2013/1613/1515/20
Correct. Of the 15 trials under the target time, 13 also had a clean exchange.
For a conditional probability, restrict the denominator to the trials that satisfy the given condition.
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Hint
Find the trials with only a clean exchange and the trials with only an under-target finish, then add them.
Pair B completed 18 clean exchanges, finished under the target time in 14 trials, and met both requirements in 12 of the 20 trials. In how many trials did Pair B meet exactly one of the two requirements?
Correct. Pair B met exactly one requirement in 8 trials.
Subtract the 12 trials with both outcomes from each individual total before adding.
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Hint
The goal requires both a clean exchange and an under-target finish in the same trial.
A student argues that Pair B should be selected because it had 18 clean exchanges compared with 16 for Pair A. Which response best uses the practice data to evaluate that claim?
The student is correct because the number of clean exchanges is the only relevant measure.Pair A is stronger for the stated goal because it met both requirements in 13 of 20 trials compared with 12 of 20 for Pair B.Pair B is stronger because 18/20 is greater than 15/20.The two pairs are equally strong because each was tested in 20 trials.
Correct. Pair A had the higher combined-event probability, 13/20 compared with 12/20.
Compare how often each pair met both requirements together, not just one requirement by itself.
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Bayrak Yarışı Takımını Oluşturmak
TR
ARC_G10_DP_02_STORY_02
Bayrak Yarışı Takımını Oluşturmak
Building the Relay Team
EN
ARC_G10_DP_02_STORY_02
Building the Relay Team