Suppose that for a recent admissions class, an Ivy League college received 2,913 applications for early admission. Of this group, it admitted 1,095 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. (a) Use the data to estimate P(E ), P(R), and P(D). If required, round your answers to four decimal places. P(E) = P(R) = P(D) = (b) Are events E and D mutually exclusive? - Select your answer -YesNoItem 4 Find P(E ∩ D). If your answer is zero, enter "0". (c) For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places. (d) Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? If required, round your answer to four decimal places.
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.
Suppose that for a recent admissions class, an Ivy League college received 2,913 applications for early admission. Of this group, it admitted 1,095 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the
| (a) | Use the data to estimate P(E ), P(R), and P(D). If required, round your answers to four decimal places. | ||||||
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| (b) | Are events E and D mutually exclusive? | ||||||
| - Select your answer -YesNoItem 4 | |||||||
| Find P(E ∩ D). If your answer is zero, enter "0". | |||||||
| (c) | For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places. | ||||||
| (d) | Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? If required, round your answer to four decimal places. | ||||||
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Suppose that for a recent admissions class, an Ivy League college received 2,825 applications for early admission. Of this group, it admitted 1,007 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the
| (a) | Use the data to estimate P(E ), P(R), and P(D). If required, round your answers to four decimal places. | ||||||
|
|||||||
| (b) | Are events E and D mutually exclusive? | ||||||
| Find P(E ∩ D). If your answer is zero, enter "0". | |||||||
| (c) | For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places. | ||||||
| (d) | Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? If required, round your answer to four decimal places. | ||||||
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