Question

A vending machine offers 8 different drinks. One day, 6 employees each purchased a drink from the vending machine. Find the probability that at least 2 employees purchased the same drink. Round your answer to the nearest hundredth.

Answer 1

each employee has 8 choices of drink,
so total # of ways they can choose = 8^6

ways in which all take different drinks = 8P6 = 8*7*6*..*3
so ways in which at least 2 take the same drink = 8^6 - 8P6

probability = (8^6 - 8P6) /8^6
= .9231

Answer 2

This can be found from the binomial distribution:
The probability of choosing a particular drink is 1/8.
\[P(0\ out\ of\ 6\ select)=(\frac{7}{8})^{6}=0.4488\]
\[P(1\ out\ of\ 6\ select)=6\times \frac{1}{8}\times(\frac{7}{8})^{5}=0.3847\]
The probability that at least 2purchase the same drink is
1 - (0.4488 + 0.3847)= ?