Suppose a basketball team had a season of games with the following characteristics:Of all the games, 60% were at-home games. Denote this by H (the remaining were away games).Of all the games, 25% were wins. Denote this by W (the remaining were losses).Of all the games, 20% were at-home wins.Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.) 0.12 0.15 0.20 0.33 0.42
Question
Suppose a basketball team had a season of games with the following characteristics:Of all the games, 60% were at-home games. Denote this by H (the remaining were away games).Of all the games, 25% were wins. Denote this by W (the remaining were losses).Of all the games, 20% were at-home wins.Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.) 0.12 0.15 0.20 0.33 0.42
Solution 1
To solve this problem, we need to find the proportion of at-home games that were wins. We know that 20% of all games were at-home wins. We also know that 60% of all games were at-home games.
So, we can set up the proportion as follows:
(At-home wins / At-home games) = (20% / 60%)
To solve for the proportion of at-home games that were wins, we divide 20% by 60%.
20% / 60% = 0.33 (rounded to two decimal places)
So, 33% of the at-home games were wins. Therefore, the correct answer is 0.33.
Solution 2
To solve this problem, we need to find the proportion of at-home games that were wins. We know that 20% of all games were at-home wins. We also know that 60% of all games were at-home games.
To find the proportion of at-home games that were wins, we divide the percentage of at-home wins by the percentage of at-home games.
So, we calculate 20% / 60% = 0.33 (rounded to two decimal places).
Therefore, the proportion of at-home games that were wins is 0.33 or 33%.
So, the correct answer is 0.33.
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