Sols3.pdf - ECOM90009 Quantitative Methods for Business...

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ECOM90009 - Quantitative Methods for Business Se cond Se mester, 201 7 Workshop 3: Probability and Discrete Distributions Solutions to Preparation Questions 1. (a) If we assume that the probability is independent of whether a family already has a boy or a girl, then the probability that the family’s other child is a girl is 1/2 or 50%. (b) Probability = 2/3. There are three ways in which the family could have at least one boy (BB, BG, GB), and only two of these involve having a girl. Each of these outcomes is equally likely. (c) The two probabilities are different because they describe different experiments. In (a) the experiment is the process of a family having a second child, and we assumed that the gender of each child is an independent event (a reasonable assumption), whereas in (b) the experiment is you observing a family, con- ditional on an event, and the events are not (cannot be) independent in this case. 2. Recall that two events are independent if knowing that one has occurred gives us no new information about the likelihood of the other occurring. 3. (a) Let A be the event in which a randomly selected person is a teenager, and let B be the event in which a randomly selected person is a casual employee. If A and B are independent, P ( A B ) = P ( A | B ) P ( B ) = P ( A ) P ( B ) 1
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P ( A ) P ( B ) = 0 . 2 × 0 . 1 = 0 . 02 (b) A person’s age and employment type are not likely to be independent, because teenagers generally find it harder to obtain a permanent job given their (relative to adults) limited skills and limited work experience.
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