One student applies for a doctoral program in Economics. The qualification of the admission depends on GRE score, GPA in his undergraduate and graduate schools, three recommendation letters, and other supportive documentations. Since this is a top program and a top university in the United States, total number of applicants is 750, but this program only admits 25 students every year. Therefore, this student claims that he has 3.3% probability to be admitted. Does this student’s claim make any sense?
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.
One student applies for a doctoral program in Economics. The qualification of the admission depends on GRE score, GPA in his undergraduate and graduate schools, three recommendation letters, and other supportive documentations. Since this is a top program and a top university in the United States, total number of applicants is 750, but this program only admits 25 students every year. Therefore, this student claims that he has 3.3% probability to be admitted. Does this student’s claim make any sense? Why or why not? Discuss and explain your reasons. You must provide your statistical analysis and reasons.
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