Question

(S) T wo hundred single-sport athletes were cross-classified according to gender, as shown in the table below. An athlete is selected at random. Male(M) Female F) ta Gender Swimmer(S) Runner(R) Cyelist(C) Total 20 115 25 85 45 200 30 20 50 65 40 105 a) What is the probability that the athlete is a male? b) What is the probability that the athlete is female and a runner? c) What is the probability that the athlete is male given that the athlete is known to be a runner? d) What is the probability that the athete is female or a swimmer or both? e) Are the events being a female and being a runner independent? Explain why or why not. n Are the events being a male and being a cyclist mutually exclusive? Explain why or why not. (9) You are a realtor considering listing a $500.000 house. The cost of advertising and providing food for other realtors during open showings is anticipated to cost you S500L. The house is quite unusual and you are given a four-month listing. If the house is unsold after four months, you lose the listing and receive nothing. You anticipate that the probability you sell your own listed house is 0.3, the probability that another agent sells your listing is 0.2, and the probability that the house is unsold after 4 months is 0.5. Ii you sell your own listed house, the commission is a hefty $30,000. If another realtor sells your listing, the commission is $15.000. The bottom line: You will not take the listing unless you anticipate carning at least s6000. Should you list the house? 10) The probability distribution of the number of accidents in North York. Ontario, each day is giveu by: p(x) 0.20 0.15 0.25 0.15 0.20 005 n this distribution, what would be the expected number of accidents on a given day and what is the approximate value of the staudard deviation of the number of accidents per day?

Answer 1