Question
James buys 4 tickets in a raffle. If his chances of winning are 1/125, how many tickets have been sold?
Answers
GPT-4o mini
Let \( x \) be the total number of tickets sold in the raffle. James buys 4 tickets, and the probability of winning with those tickets is given by the formula:
\[
\text{Probability of winning} = \frac{\text{Number of tickets bought}}{\text{Total number of tickets sold}} = \frac{4}{x}
\]
According to the problem, his chances of winning are \( \frac{1}{125} \). Setting the two expressions equal gives us:
\[
\frac{4}{x} = \frac{1}{125}
\]
To find \( x \), we can cross-multiply:
\[
4 \cdot 125 = 1 \cdot x
\]
Calculating \( 4 \cdot 125 \):
\[
4 \cdot 125 = 500
\]
Thus, we have:
\[
x = 500
\]
So, the total number of tickets sold is
\[
\boxed{500}
\]
\[
\text{Probability of winning} = \frac{\text{Number of tickets bought}}{\text{Total number of tickets sold}} = \frac{4}{x}
\]
According to the problem, his chances of winning are \( \frac{1}{125} \). Setting the two expressions equal gives us:
\[
\frac{4}{x} = \frac{1}{125}
\]
To find \( x \), we can cross-multiply:
\[
4 \cdot 125 = 1 \cdot x
\]
Calculating \( 4 \cdot 125 \):
\[
4 \cdot 125 = 500
\]
Thus, we have:
\[
x = 500
\]
So, the total number of tickets sold is
\[
\boxed{500}
\]