Before the championship relay, Emek and Tara compared two possible runner lineups using results from 30 recent practice races for each lineup. The team needed both a fast start and a successful finish. Lineup A had a fast start in 21 races and a successful finish in 24, but both events occurred together in only 17 races. Lineup B had a fast start in 19 races and a successful finish in 23, with both occurring together in 18 races. At first, Emek noticed that Lineup A had the higher individual rates for both fast starts and successful finishes. Tara pointed out that the championship required both conditions in the same race, so those separate statistics were not enough. They calculated the combined-event probabilities: 17/30 for Lineup A and 18/30 for Lineup B. Although Lineup B had fewer fast starts overall, its 60% probability of meeting both requirements was greater than Lineup A's probability of about 56.7%. They selected Lineup B, confident that considering the combined events gave them the stronger championship strategy.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Subtract the number of races with both events from the number with a fast start.
For Lineup A, a fast start occurred in 21 of 30 races, and both a fast start and a successful finish occurred in 17 races. What is the probability that Lineup A had a fast start but did not also have a successful finish?
4/3017/3021/3038/30
Correct. There were 4 races with a fast start but not both events, giving a probability of 4/30.
Separate the races with only a fast start from the 17 races in which both events occurred.
Next
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Hint
The 18 races with both events are included among the 23 successful finishes.
Lineup B had a successful finish in 23 of its 30 races, and both a fast start and a successful finish occurred in 18 races. In how many races did Lineup B have a successful finish without also having a fast start?
Correct. Lineup B had 5 successful finishes without a fast start.
Subtract the number of races with both events from the total number of successful finishes.
Next
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Hint
The championship strategy depends on both requirements happening together, not on either event by itself.
Which statement best explains why Lineup B was chosen even though Lineup A had more fast starts and more successful finishes overall?
Lineup B had more practice races than Lineup A.Lineup B had a higher probability of a fast start by itself.Lineup B had a higher probability that both required events occurred in the same race.Lineup B had fewer successful finishes, so it was less likely to make mistakes.
Correct. Lineup B met both requirements together in 18 of 30 races, compared with 17 of 30 for Lineup A.
Focus on the combined event: a fast start and a successful finish occurring in the same race.
Next
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Final Bayrak Yarışını Planlamak
TR
ARC_G09_DP_02_STORY_02
Final Bayrak Yarışını Planlamak
Planning the Final Relay
EN
ARC_G09_DP_02_STORY_02
Planning the Final Relay