Question

Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered

Answer 1

18.59% probability that EXACTLY 10 will show that the above three food items were ordered

Explanation:

For each customer, there are only two possible outcomes. Either they order the above food items, or they do not. The probability of a customer ordering these items is independent of other customers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink.

This means that
`p = 0.6`

If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered

This is P(X = 10) when n = 15. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 10) = C_(15,10).(0.6)^(10).(0.4)^(5) = 0.1859`

18.59% probability that EXACTLY 10 will show that the above three food items were ordered