During a tennis tournament, Tara and Emek studied the possible routes their teammate could take to the final. First, their teammate had a 0.8 probability of winning the quarterfinal. Meanwhile, another match would determine the semifinal opponent: Player A had a 0.6 probability of advancing, while Player B had a 0.4 probability. If their teammate reached the semifinal, past results suggested a 0.7 probability of defeating Player A but a 0.5 probability of defeating Player B. Tara organized the possibilities in a tree diagram. Emek multiplied probabilities along each route. The probability of reaching the final by facing Player A was 0.8 x 0.6 x 0.7 = 0.336, while the route through Player B had probability 0.8 x 0.4 x 0.5 = 0.160. Adding these paths gave an overall probability of 0.496, or 49.6%, of reaching the final. Since the route through Player A was more likely, they recommended spending more practice time preparing for that matchup while still reviewing tactics for Player B.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
To reach the final through Player A, every event along that route must occur.
A student says the probability of reaching the final through Player A is 0.6 x 0.7 = 0.42. What did the student forget to include?
The 0.4 probability that Player B advancesThe 0.8 probability that the teammate wins the quarterfinalThe 0.5 probability of defeating Player BThe probability of losing the quarterfinal
Correct. The teammate must first win the quarterfinal, so the factor 0.8 must also be included.
Follow the full path from the quarterfinal to the final and include every probability along that route.
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Hint
Multiply the probability 0.496 by 1000.
Out of 1000 similar tournaments, about how many times would the teammate be expected to reach the final using the overall probability of 0.496 from the story?
Correct. An overall probability of 0.496 corresponds to about 496 out of 1000 tournaments.
Convert the probability into an expected count by multiplying by the number of tournaments.
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Hint
Weight the semifinal win probability by which opponent advances, then multiply by the probability of reaching the semifinal.
Emek checks the calculation by finding the probability of reaching the semifinal first and then the probability of winning the semifinal given that the teammate gets there. Which calculation correctly reproduces the overall probability of reaching the final?
0.8 x (0.6 + 0.7 + 0.4 + 0.5)0.8 x (0.6 x 0.7 + 0.4 x 0.5)(0.8 x 0.6) + (0.7 x 0.4)0.8 + (0.6 x 0.7) + (0.4 x 0.5)
Correct. The weighted semifinal probability is 0.6 x 0.7 + 0.4 x 0.5, and multiplying by 0.8 gives 0.496.
The two possible semifinal opponents form separate branches, so multiply along each branch and add the branch results.
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Turnuva Tahminini Yorumlamak
TR
ARC_G10_DP_02_STORY_03
Turnuva Tahminini Yorumlamak
Reading the Tournament Forecast
EN
ARC_G10_DP_02_STORY_03
Reading the Tournament Forecast