Rob Rales is preparing a report that his employer, the Titre Corporation, will eventually deliver to the Federal Aviation Administration. First, the report must be approved by Rob’s group leader, department head, and division chief (in that order). Rob knows from experience that the three managers act independently. Further, he knows that his group leader approves 85 percent of his reports, his department head approves 80 percent of the reports written by Rob that reach him, and his division chief approves 82 percent of Rob’s work. (a) What is the probability that the first version of Rob’s report is submitted to the FAA? (b) What is the probability that the first version of Rob’s report is approved by his group leader and department head, but is not approved by his division chief?
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.
Rob Rales is preparing a report that his employer, the Titre Corporation, will eventually
deliver to the Federal Aviation Administration. First, the report must be approved by
Rob’s group leader, department head, and division chief (in that order). Rob knows from
experience that the three managers act independently. Further, he knows that his group
leader approves 85 percent of his reports, his department head approves 80 percent of
the reports written by Rob that reach him, and his division chief approves 82 percent of
Rob’s work.
(a) What is the probability that the first version of Rob’s report is submitted to the FAA?
(b) What is the probability that the first version of Rob’s report is approved by his group
leader and department head, but is not approved by his division chief?
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