Question

An airline has classified its customers as high-volume travelers (assumed to be business travelers) or low-volume travelers (assumed to be leisure travelers). Eight-five (85) percent are high volume travelers. If five people are randomly selected from a list of customers, what is the probability all are high-volume (business) travelers?

Answer 1

The probability that the 5 travelers chosen are high volume travelers is 0.4437

Explanation:

The number of people who are high volume travelers, in the random sample of 5 people, is a binomial random variable
`X` with probability of success
`p = 0.85`,
`n = 5`. Therefore, the model is
`{5 \choose x} (0.85)^(x)(0.15)^((5-x))`. So, you have:

`P (X = 5) = {5 \choose 5}(0.85)^(5)(0.15)^(0) = 0.4437`.

The probability that the 5 travelers chosen are high volume travelers is 0.4437

Answer 2

The probability is 44.37%.

Explanation:

The probability for a given customer to belong to the business class is given by:

`P(B)=0.85`

Since each event is independent we'll obtain the probability as follows:

`P(BBBBB) = P(B)* P(B) * P(B)* P(B)* P(B)= 0.85^5=0.4437`

Therefore the probability that 5 customers chosen from a randomly selected list of customers all belong to the business class is of 44.37%.