A hotel operates a shuttle bus between the hotel and the airport. The maximum capacity of the hotel’s minivan is 10 passengers. On each trip from the airport, the manager of the hotel conducts the experiment of noting the number of people in the minivan.a) What is an appropriate sample space for this experiment?b) Describe the event “fewer than 5 people were in the minivan.”
Please show more than one approach.
a) The sample space for this experiment is the set of all possible outcomes or combinations of passengers in the minivan. Since the maximum capacity of the minivan is 10, the sample space can be represented as {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Each number represents the count of people in the minivan.
b) Approach 1: The event "fewer than 5 people were in the minivan" can be described mathematically as {0, 1, 2, 3, 4}. This means that the count of people in the minivan is any number from 0 to 4.
Approach 2: Another way to describe the event "fewer than 5 people were in the minivan" is as the complement of the event "5 or more people were in the minivan." The complement of an event A, denoted as A', represents all outcomes that are not in A. In this case, the event "5 or more people were in the minivan" can be represented as {5, 6, 7, 8, 9, 10}. Therefore, the event "fewer than 5 people were in the minivan" can be represented as {0, 1, 2, 3, 4}, which is the complement of {5, 6, 7, 8, 9, 10}.
Both approaches describe the event "fewer than 5 people were in the minivan" accurately, with one approach listing the specific numbers (0 to 4) and the other approach using the concept of complements.