With one minute left in a close basketball game, Tara and Emek compared two possible plays. For Strategy A, team statistics showed a 0.80 probability of completing a pass, followed by a 0.65 probability of making the shot. Their tree diagram gave a success probability of 0.80 times 0.65 = 0.52. Strategy B offered two ways to score: a direct shot with probability 0.38, or, if that shot missed with probability 0.62, a rebound followed by a second shot. The probability of securing the rebound was 0.50, and the probability of making the second shot was 0.55. Emek calculated the second scoring path as 0.62 times 0.50 times 0.55 = 0.1705. Adding the two successful paths gave Strategy B a probability of 0.5505. Since 0.5505 was greater than 0.52, Tara and Emek recommended Strategy B. The team followed the plan and created the scoring opportunity it needed.

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Both events on this successful path must occur, so use the probabilities along the path together.
For Strategy A, the team must first complete a pass with probability 0.80 and then make a shot with probability 0.65. Which calculation gives the probability that Strategy A succeeds?
0.80 + 0.65 = 1.450.80 - 0.65 = 0.150.80 times 0.65 = 0.521 - 0.80 times 0.65 = 0.48
Correct! Multiplying the probabilities along the successful path gives 0.52.
Not quite. Since the pass and then the shot must both succeed, multiply the two probabilities.
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Hint
Multiply the probability of success by the number of situations.
Strategy B has a success probability of 0.5505. If the team could use Strategy B in 2000 situations with the same probabilities, how many successful scoring plays would be expected?
Correct! A probability of 0.5505 over 2000 situations gives an expected 1101 successes.
Try again. Multiply 0.5505 by 2000 to find the expected number of successful plays.
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Hint
Multiply probabilities within the rebound scoring path, then combine that path with the separate direct-shot scoring path.
Strategy B can score either on the direct shot with probability 0.38 or after a missed shot, rebound, and successful second shot. Which expression correctly represents the total probability that Strategy B scores?
0.38 times 0.62 times 0.50 times 0.550.38 + 0.62 + 0.50 + 0.550.38 times 0.55 + 0.62 times 0.500.38 + (0.62 times 0.50 times 0.55)
Correct! The two different successful paths are combined by adding their probabilities.
Not quite. Multiply the probabilities along the rebound path first, then add its probability to the direct-shot probability.
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Son Dakika Oyunu
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ARC_G11_DP_02_STORY_01
Son Dakika Oyunu
The Final-Minute Play
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ARC_G11_DP_02_STORY_01
The Final-Minute Play