With seconds left in a championship basketball game, Tara and Emek helped evaluate two possible plays that could produce the two points their team needed. From earlier games, they built a probability model for each sequence. In Play A, the opening pass reached the intended player 85% of the time. When that pass succeeded, the player made the shot 60% of the time. Tara calculated the probability of completing both events as 0.85 times 0.60 = 0.51. Play B used a more difficult pass that succeeded 75% of the time, but after a successful pass, the shooter scored 72% of the time. Emek found its overall success probability: 0.75 times 0.72 = 0.54. Although Play A had the more reliable pass, its complete sequence was less likely to produce the needed basket. They checked that the shooting probabilities were conditional on successful passes rather than separate independent events. Since 54% exceeded 51%, Tara and Emek recommended Play B. The team followed the higher-probability plan for its final possession.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
The shot can occur successfully only after the pass succeeds, so use the probability of the pass and the conditional probability of the shot.
Which expression correctly represents the probability that Play B ends with a successful basket?
0.75 + 0.720.75 times 0.720.72 / 0.751 - (0.75 times 0.72)
Correct. Multiply the probability of the successful pass by the probability of scoring after that pass.
Not quite. The complete play requires both the pass and the shot to succeed in sequence.
Next
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Hint
Multiply the number of trials by the probability of success for Play A.
Suppose the team could run Play A 200 times under similar conditions. Based on its success probability of 0.51, how many successful baskets would the model predict on average?
Correct. The model predicts about 102 successful baskets in 200 attempts.
Check that you multiply 200 by Play A's overall success probability, 0.51.
Next
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Hint
Multiply 0.85 by 0.65, then compare the result with Play B's 0.54.
A coach proposes a revised Play A with the same 85% pass success rate but an improved conditional shooting probability of 65%. Which statement correctly compares the revised Play A with Play B?
Revised Play A has success probability 0.5525, so it is more likely to succeed than Play B.Revised Play A has success probability 0.50, so it is less likely to succeed than Play B.Revised Play A has success probability 0.85 + 0.65 = 1.50, so it is more likely to succeed than Play B.Revised Play A has success probability 0.65, so it is more likely to succeed than Play B.
Correct. The revised Play A would have a 55.25% success probability, which exceeds Play B's 54%.
Not quite. Find the probability that both stages of the revised play succeed, then compare it with 0.54.
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Son Oyunu Planlamak
TR
ARC_G12_DP_02_STORY_01
Son Oyunu Planlamak
Planning the Final Play
EN
ARC_G12_DP_02_STORY_01
Planning the Final Play