Question

Frozen Taste ice cream factory wants to analyze if the customers like its new flavor, peanut butter chocolate chip. The probability that a customer likes the new flavor is .83. If a customer is asked to taste the flavor twice within 4 hours, then what is the probability that a customer likes this flavor the first time and the second time

Answer 1

0.6889 = 68.89% probability that a customer likes this flavor the first time and the second time

Explanation:

For each time the customer is asked, there are only two possible outcomes. Either they like the flavor, or they do not. Each event is independent of each other. 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.

The probability that a customer likes the new flavor is .83.

This means that
`p = 0.83`

What is the probability that a customer likes this flavor the first time and the second time

This is P(X = 2) when n = 2. So

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

`P(X = 2) = C_(2,2).(0.83)^(2).(0.17)^(0) = 0.6889`

0.6889 = 68.89% probability that a customer likes this flavor the first time and the second time