Question
At the Hamilton County Fair, 6 of the last 16 people to spin the prize wheel won a prize. Considering this data, how many of the next 48 players would you expect to win a prize?
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Answers
GPT-4o mini
To find the expected number of winners among the next 48 players, you can first determine the winning percentage based on the past data.
The probability (P) of winning a prize based on the last 16 players is:
\[
P(\text{winning}) = \frac{\text{Number of winners}}{\text{Total players}} = \frac{6}{16} = 0.375
\]
Now, to find the expected number of winners among the next 48 players, you can multiply the total number of players by the winning probability:
\[
\text{Expected winners} = P(\text{winning}) \times \text{Number of players} = 0.375 \times 48
\]
Calculating this gives:
\[
\text{Expected winners} = 0.375 \times 48 = 18
\]
Therefore, you would expect **18** of the next 48 players to win a prize.
The probability (P) of winning a prize based on the last 16 players is:
\[
P(\text{winning}) = \frac{\text{Number of winners}}{\text{Total players}} = \frac{6}{16} = 0.375
\]
Now, to find the expected number of winners among the next 48 players, you can multiply the total number of players by the winning probability:
\[
\text{Expected winners} = P(\text{winning}) \times \text{Number of players} = 0.375 \times 48
\]
Calculating this gives:
\[
\text{Expected winners} = 0.375 \times 48 = 18
\]
Therefore, you would expect **18** of the next 48 players to win a prize.