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% owere wins. Denote this by W (the remaining were losses).Of all the games, 20% were at-home wins.If the team won a game, how likely is it that this was a home game? (Note: Some answers are rounded to 2 decimal places.) 0.05 0.12 0.15 0.42 0.80
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% owere wins. Denote this by W (the remaining were losses).Of all the games, 20% were at-home wins.If the team won a game, how likely is it that this was a home game? (Note: Some answers are rounded to 2 decimal places.) 0.05 0.12 0.15 0.42 0.80
Solution 1
To solve this problem, we need to use the concept of conditional probability.
The question is asking for the probability that a game was a home game given that the team won. This can be denoted as P(H|W).
We know that P(H ∩ W) = 0.20, which is the probability of home wins. We also know that P(W) = 0.25, which is the probability of wins.
The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B).
Substituting the given values into the formula, we get:
P(H|W) = P(H ∩ W) / P(W) = 0.20 / 0.25 = 0.80
So, if the team won a game, the probability that it was a home game is 0.80. Therefore, the correct answer is 0.80.
Solution 2
To solve this problem, we need to use the concept of conditional probability.
We are given that:
- P(H) = Probability of home games = 60% = 0.60
- P(W) = Probability of wins = 25% = 0.25
- P(H ∩ W) = Probability of home wins = 20% = 0.20
We are asked to find P(H|W), which is the probability that the game was a home game given that the team won.
The formula for conditional probability is:
P(H|W) = P(H ∩ W) / P(W)
Substituting the given values into the formula, we get:
P(H|W) = 0.20 / 0.25 = 0.80
So, if the team won a game, there is an 80% chance that it was a home game. Therefore, the correct answer is 0.80.
Similar Questions
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