Answer to Question #115899 in Statistics and Probability for Nat

Question

A store is having a contest. Gold tickets worth $100 are hidden in 5 of 500 coffee cups. When you buy a coffee, a cup is selected and given to you to take home.
If you buy two coffees per day over the course of two weeks, what is the probability that you will win at least one ticket?

Answer 1

Let $X=$ the number of winning tickets: $X\sim Bin(n,p)$

$$p(x)=P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}$$

Given

$$p={5\over 500}=0.01, n=2\cdot14=28$$

The probability that you will win at least one ticket is

$$P(X\geq1)=1-P(X=0)=$$

$$=1-\binom{28}{0}0.01^0(1-0.01)^{28-0}\approx0.24528$$