Question

There is a 0. 33 probability that a random passenger on United airlines flight is a member of their frequent flyer program. An agent asks passengers boarding a flight if they are a member of the frequent flyer program

A) explain what the 0. 33 probability means in this setting.


b) does this probability say that if 100 passengers are asked if they are members of the frequent flyer program that exactly 33 of them are? Explain your answer

Answer 1

A) The 0.33 probability means that if the agent asks a large number of passengers on United airlines flights, about 33% of them will be members of the frequent flyer program. It does not mean that exactly one out of every three passengers will be a member, but rather that this is the long-run relative frequency of members among all passengers12

B) No, this probability does not say that if 100 passengers are asked, exactly 33 of them are members. This is because the number of members among 100 passengers is a random variable that can vary from sample to sample. The probability only tells us the expected value or the average number of members in many samples of 100 passengers. It is possible, but not very likely, that none or all of the 100 passengers are members. The actual number of members will depend on how the 100 passengers are selected and how representative they are of the population of all passengers

Explanation: