Probability of Selling planes in Pioneer Aircraft Co.
Determine the probability of each number of planes sold—of 0, 1, 2, and 3— in a 50-week period
Probability is the science of assigning numerical figures to the possible occurrence of an event from a random experiment, which are often collectively unique (Probability. OPRE 6301). Since its conception, probability holds two varying views. Its’ statistical perspective is inclined towards coming up with unbiased mathematical guidelines that rule the processes (Batanero et al., 2016). Therefore, it assigns values from data established in experiments and surveys. On the flip side, the epistemic view presents a notion that probability is the extent of belief of an individual that is relying on the amount of information accessed by the person allocating probability (Batanero et al., 2016).
From Pioneer Aircraft Co, these are probabilities for the specific number of planes that were sold.
PLANES SOLD WEEKS THIS NUMBER SOLD PROBABILITY
0 40 40/50=0.8
1 8 8/50=0.16
2 1 1/50=0.02
3 1 1/50=0.02
Decide what approach is best used to determine probability.
The appropriate method of determining probability from the data presented by the Pioneer Aircraft Co is the relative frequency approach. This decision was arrived at following the examination of the various approaches in determining probability.
Distinguish between the approaches to make it clear that the approach used was the best fit for these airplane sales.
Classical approach
The initial concept in this approach to determining probability was associated with games where winning or losing was predominantly linked to chances. It involved games like tossing a dice. This theory is structured from the perception that any possible occurrence was equiprobable (Batanero et al., 2016). It found its strength from the pre-established notion that the concept is having a lot of sense in games of chance. For instance, a football coach can advise players to put into consideration the available options of occurrence and the possibility of achieving the desired results. The comparison can assist them in coming up with a sound and fair bet.
Further, the perpetrators of this approach posit that probability is a fraction of the number of occurrences to an event divided by the total number of possible events (Batanero et al., 2016). This definition was subject to rejection from various opposing views. They mainly arose from the proclamation that the equiprobability assumption is biased and hampers the involvement of probability in various forms of natural occurrences. These opposing views have orchestrated the development of other approaches to defining and establishing probability.
Relative Frequency Approach
The frequency approach stems from the fact that probability is estimated from the available historical data or the results of an experiment (Probability. OPRE 6301). It is also built on the precept that relative frequencies of an occurrence usually merge at a constant estimate. It often follows an independent uniform examination of arbitrary experiments. Moreover, this approach is backed by the Law of Large Numbers, which was extended by Bernouli. It proclaims that the frequency n of an event in several successive trials is supposed to be close to the abstract probability P (Batanero et al., 2016). Furthermore, probability draws closer to the pre-established value when more experimentations are carried out. This law is proof of the unbiased feature of probability. It is backed up by consistent frequencies, which are established form the ensuing experiments.
From the characteristics exhibited above, this approach describes probability as a random experiment that is conducted infinitely to obtain frequencies which are directed towards an initially established theoretical number (Batanero et al., 2016). The definition increased the possibility of applying this approach in various areas. Which includes insurance and the determination of life expectancy. However, the approach is also subjected to scrutiny since not all of its proclamations are not objective. For instance, the values obtained from the possible occurrence of an event are estimates which are different from one experiment to the other. Moreover, some are experiments cannot be conducted under constant conditions, which makes this approach inefficient (Batanero et al., 2016). The latter claim also relates to the fact that it is not convenient to carry out an experiment to an infinite number of times (Probability. OPRE 6301).
Subjective Approach
From a subjective approach, the probability is described as the extent of belief an individual abhors towards the possibility of an event (Probability. OPRE 6301). Therefore, the framework for declaring a probability is judgment. From the two approaches discussed, the classical approach had some element of subjectivity when coming up with the probability of a simple event. However, this approach has some slight difference, which is attached to the perception that it is often confined to experiments that cannot be repeated (Probability. OPRE 6301). An example experiment is the prediction of prices in the stock market of the determination of a winner in a horse race before the experiment.
This approach was developed from Bayes’ theorem. It claims that a previous probability is predisposed to change when employing new statistics (Batanero et al., 2016). It also implores that the probability will drop its objective feature since it relies on old data to make judgments. Keynes, Ramsey, and de Finetti came up with the earlier highlighted definition from the theorem postulated by Bayes (Batanero et al., 2016). From this point of view, there is no need to carry out the same experiment to arrive at a certain probability. This nature of the subjective approach paved the way for its entry into the fields of economy and politics. Those areas are subject to situations that take place once. The qualities showcased have gained entry for the Bayesian theory in major areas of inferences within contemporary society.
Determine if the approach would change if we also needed to track sales of some planes with GPS installed.
The relative frequency approach will still uphold if we are to track the sales of planes with GPS installed. The approach is considered the most credible when compared with the other two approaches discussed. The main reason stems from the fact that it employs a new set of data in determining the probability of a particular situation. This quality distinguishes the approach from the other two, which have elements of subjective analysis in their determination of probability.
References
Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on teaching and learning probability. In Research on teaching and learning probability (pp. 1-33). Springer, Cham. https://www.researchgate.net/publication/305215333_Research_on_Teaching_and_Learning_Probability
Probability. OPRE 6301. https://personal.utdallas.edu/~scniu/OPRE-6301/documents/Probability.pdf