The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 32 cookies. What is the probability she will not win the dinner for two? Write your answer as a fraction in simplest form, if one exists.

Question

Quizplus · Accepted Answer

The probability that Lisa will not win is the probability that none of her 32 cookies is the winning one. There are 718 cookies in total, so the probability that a specific cookie is not the winner is $\frac{717}{718}$. The probability that all 32 of her cookies are not winners is $\left(\frac{717}{718}\right)^{32}$, which simplifies to $\frac{343}{359}$.

The College Hiking Club Is Having a Fund Raiser to Buy