Before their basketball semifinal, Tara and Emek reviewed data from 40 recent games to choose between two opening plays. Play A had been used in 20 games. The team won the opening tip in 13 of those games and scored on its first possession in 12, with both events occurring in 9 games. Play B had also been used in 20 games. The team won the tip in 11 games and scored first in 14, with both events occurring in 10 games. At first, Tara noticed that Play A had the higher probability of winning the tip: 13/20 compared with 11/20. Emek pointed out that a successful start required both winning the tip and scoring on the first possession. The combined probability was 9/20, or 45%, for Play A and 10/20, or 50%, for Play B. Although Play B was associated with fewer tip wins, it had the stronger record for achieving both outcomes together. They recommended Play B, giving the team a data-based plan for the opening minutes.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Because the team is known to have won the tip, use the 13 tip-win games as the new total.
For Play A, the team won the opening tip in 13 of 20 games, and in 9 games it both won the tip and scored on the first possession. What is the probability that the team scored on the first possession given that it won the opening tip?
9/209/1312/2013/20
Correct. Of the 13 games with a tip win, 9 also had a score on the first possession.
For a conditional probability, restrict the total to the games in which the given condition occurred.
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Hint
First find how many games had at least one of the two events, making sure not to count the 9 games with both events twice.
For Play A, the team won the opening tip in 13 games, scored on the first possession in 12 games, and did both in 9 of the 20 games. In how many games did neither event occur?
Correct. Neither event occurred in 4 games.
Use inclusion-exclusion to find the number of games with at least one event, then subtract from 20.
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Hint
The 10 games in which both events occurred are part of the 11 games with a tip win.
For Play B, the team won the opening tip in 11 games and both won the tip and scored on the first possession in 10 games. Which statement is correct about games in which Play B won the tip?
The team scored on the first possession in 10 of the 11 games in which it won the tip.The team scored on the first possession in exactly half of the games in which it won the tip.The team failed to score on the first possession in 10 of the 11 games in which it won the tip.The story does not provide enough information to connect tip wins with first-possession scores.
Correct. Of the 11 tip-win games for Play B, 10 also included a score on the first possession.
Use the overlap of 10 games and compare it with the 11 games in which Play B won the tip.
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Açılış Oyununu Seçmek
TR
ARC_G10_DP_02_STORY_01
Açılış Oyununu Seçmek
Choosing the Opening Play
EN
ARC_G10_DP_02_STORY_01
Choosing the Opening Play