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Chapter 7: Problem 41

A certain airport hotel operates a shuttle bus service between the hotel and the airport. The maximum capacity of a bus is 20 passengers. On alternate trips of the shuttle bus over a period of \(1 \mathrm{wk}\), the hotel manager kept a record of the number of passengers arriving at the hotel in each bus. a. What is an appropriate sample space for this experiment? b. Describe the event \(E\) that a shuttle bus carried fewer than ten passengers. c. Describe the event \(F\) that a shuttle bus arrived with a full load.

Short Answer

Expert verified
a. The appropriate sample space for this experiment is: \(S = \{0, 1, 2, 3, ..., 18, 19, 20\}\) b. The event E, a shuttle bus carrying fewer than ten passengers, can be described as: \(E = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\) c. The event F, a shuttle bus arriving with a full load, can be described as: \(F = \{20\}\)

Step by step solution

01

Define the Sample Space

The sample space should represent all possible numbers of passengers on the bus during a single trip. Since the maximum capacity of the bus is 20 passengers, the sample space for this experiment will be the set of all possible numbers of passengers, starting from 0 passengers to 20 passengers: \(S = \{0, 1, 2, 3, ..., 18, 19, 20\}\)
02

Describe Event E - Fewer Than 10 Passengers

Now, we need to describe the event E which occurs when the bus is carrying fewer than ten passengers. In this case, we can define the event simply as the subset of the sample space containing the number of passenger cases where there are fewer than ten passengers in the bus. Event E: Fewer than 10 passengers on the bus. \(E = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\)
03

Describe Event F - Full Load of Passengers

Finally, we'll describe event F, which is when the bus arrives with a full load. This event can be described as the subset of the sample space consisting of only one element, the number 20 since the bus is fully loaded when it carries its maximum capacity of 20 passengers. Event F: Full load of passengers. \(F = \{20\}\)

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