Two hundred people apply for three jobs. Forty of the applicants are women. (a) If three people are selected at random, what is the probability that all are women? (Round your answer to six decimal places.) (b) If three people are selected at random, what is the probability that two are women? (Round your answer to six decimal places.) (c) If three people are selected at random, what is the probability that one is a woman? (Round your answer to six decimal places.) (d) If three people are selected at random, what is the probability that none is a woman? (Round your answer to six decimal places.) (e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why? No, the probabilities do not indicate the presence of gender discrimination because in the hiring process all outcomes are equally likely. Yes, the probabilities indicate the presence of gender discrimination. The probabilities do not indicate the presence or absence of gender discrimination. For the employer to choose the most appropriate person for the job means that not all events are equally likely.
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.
Two hundred people apply for three jobs. Forty of the applicants are women.
(b) If three people are selected at random, what is the probability that two are women? (Round your answer to six decimal places.)
(c) If three people are selected at random, what is the probability that one is a woman? (Round your answer to six decimal places.)
(d) If three people are selected at random, what is the probability that none is a woman? (Round your answer to six decimal places.)
(e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why?
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