Question
At the Hamilton County Fair, 5 of the last 12 people to spin the prize wheel won a prize. Considering this data, how many of the next 60 players would you expect to win a prize?
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Answers
GPT-4o mini
To find the expected number of people who would win a prize out of the next 60 players at the Hamilton County Fair, we can use the probability of winning a prize based on the data provided.
From the data, 5 out of the last 12 people won a prize. Therefore, the probability \( P \) of winning a prize is:
\[
P = \frac{5}{12}
\]
Next, we can calculate the expected number of winners among the next 60 players by multiplying the total number of players by the probability of winning:
\[
\text{Expected winners} = P \times \text{Total players} = \frac{5}{12} \times 60
\]
Now, performing the calculation:
\[
\text{Expected winners} = \frac{5 \times 60}{12} = \frac{300}{12} = 25
\]
Thus, you would expect **25 people** out of the next 60 players to win a prize.
From the data, 5 out of the last 12 people won a prize. Therefore, the probability \( P \) of winning a prize is:
\[
P = \frac{5}{12}
\]
Next, we can calculate the expected number of winners among the next 60 players by multiplying the total number of players by the probability of winning:
\[
\text{Expected winners} = P \times \text{Total players} = \frac{5}{12} \times 60
\]
Now, performing the calculation:
\[
\text{Expected winners} = \frac{5 \times 60}{12} = \frac{300}{12} = 25
\]
Thus, you would expect **25 people** out of the next 60 players to win a prize.