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# Pioneer Aircraft: Probability of Planes Sold

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Pioneer Aircraft Co. sells private, single-engine planes. Most sales are for customers engaged in private and leisure flying. In a 50-week period, sales in the past five years have averaged to the following:

PLANES SOLD WEEKS THIS NUMBER SOLD
0 40
1 8
2 1
3 1

1. Determine the probability of each number of planes sold—of 0, 1, 2, 3—in a 50-week period. (Pioneer sales office is closed the other two weeks of the year.)

2. Decide what approach (objective approach, subjective approach, relative frequency approach) is best used to determine probability. Distinguish between the approaches to make it clear that the approach used was the best fit for these airplane sales.

3. Determine if the approach would change if we also needed to track sales of some planes with GPS installed.

#### Solution Preview

1.
The probability of each number of planes sold of 0,1,2, or 3 in a 50 week sales office can be determined using the ratio of occurrence of a singular event and the total number of outcomes. This tool can be used because data has been collected in the past and the average is given to us (1). Based on the past data the probability of selling 0 planes is (40 divided by 50) = 0.8, the probability of selling 1 plane is (8 divided by 50) = 0.16, the probability of selling 2 planes is (1 divided by 50) = 0.02, and the probability of selling 1 plane is (1 divided by 50) = 0.02.

2.
The best approach to determine probability is the objective approach. In the objective approach the analysis is based on a recorded observation rather than a subjective estimate. Objective probabilities are a more accurate because these are based on actual observations. The objective approach to probability is the best approach to determine probability because it is based on actual measurements, statistics, and experiments. In financial analysis it is important to use objective probability so that emotional decisions are avoided when investing money (2). Objective probability means that the event will occur is based on a calculation in which each measure is a recorded observation, rather than an estimate. For example, one can find ...

#### Solution Summary

The response provides you a structured explanation of Pioneer Aircraft and approaches to probability. It also gives you the relevant references.

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