James buys 4 tickets in a raffle. If his chances of winning are 1/125, how many tickets have been sold?

Answer 1

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

$$\boxed{{\displaystyle 500}}$$