On-Time Performance of Airlines. The Bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, United, and US Airways share terminal C at Boston’s Logan Airport. Suppose that the percentage of on-time flights reported was 76.8% for JetBlue, 71.5% for United, and 82.2% for US Airways. Assume that 30% of the flights arriving at terminal C are JetBlue flights, 32% are United flights, and 38% are US Airways flights. Develop a joint probability table with three rows (the airlines) and two columns (on-time and late). Answer Let Given: Joint probabilities using the multiplication law With the marginal probabilities , , and given, the joint probability table can then be shown as follows. An announcement is made that Flight 1382 will be arriving at gate 20 of terminal C. What is the probability that Flight 1382 will arrive on time? Answer Using the joint probability table, the probability of an on-time flight is the marginal probability What is the most likely airline for Flight 1382? What is the probability that Flight 1382 is by this airline?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
On-Time Performance of Airlines. The Bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, United, and US Airways share terminal C at Boston’s Logan Airport. Suppose that the percentage of on-time flights reported was 76.8% for JetBlue, 71.5% for United, and 82.2% for US Airways. Assume that 30% of the flights arriving at terminal C are JetBlue flights, 32% are United flights, and 38% are US Airways flights.
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Develop a joint
probability table with three rows (the airlines) and two columns (on-time and late).AnswerLet
Given:
Joint probabilities using the multiplication law
With the marginal probabilities , , and given, the joint probability table can then be shown as follows.
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An announcement is made that Flight 1382 will be arriving at gate 20 of terminal C. What is the probability that Flight 1382 will arrive on time?
AnswerUsing the joint probability table, the probability of an on-time flight is the marginal probability
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What is the most likely airline for Flight 1382? What is the probability that Flight 1382 is by this airline?
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