“A" qualifier (qualifying marathon time) In the 2016 US Women's Olympic marathon trials, there were 149 finishers. The "B" qualifier (qualifying marathon time) "B" qualifier (qualifying half- marathon time) women qualified either by running a qualifying marathon time or a qualifying half marathon time. "A" qualifiers had a marathon qualifying time of 2:37:00 or faster; "B" qualifiers had either a marathon qualifying time of 2:37:01 - 2:45:00 or a half-marathon qualifying time of 1:15:00 or faster. The table summarizes t athletes by qualifying race and by finishing time in the trials race. finishing time 2:40:00 or faster 10 1 finishing time 2:40:01 to 3:00:00 11 75 19 105 finishing time 3:00:01 or slower 1 25 29 22 104 23 An athlete is selected at random from the finishers. Find the probability that: (note : some are overall probabilities; some are conditional. Read carefully!) b) the athlete finished in 3:00:01 or slower a) the athlete was a "B" qualifier c) the athlete finished in 2:40:00 or faster and was an "A" qualifier d) the athlete was a "B" qualifier and finished in 2:40:01 or slower e) the athlete ran a half-marathon qualifying time or finished in 3:00:01 or slower the athlete was an "A" qualifier given that f) they finished in 2:40:00 or faster g) the athlete finished in 2:40:00 or faster given that they were an "A" qualifier h) the athlete finished in 2:40:01 or slower given that they were a "B" qualifier j) the athlete was an "A" qualifier given that they finished in 2:40:01 or slower the athlete was an "A" qualifier, given that i) they qualified with a marathon time. Sources : http://www.marathonguide.com/news/exclusives/2016USAOlympicTeamTrialsMarathon/MensWomensOlympicMarathonTnaisodana and https://www.runnerspace.com/gprofile.php?mgroup id%3D45365&do3Dnews&news id%=394996 Check your answers (not in order) : 0.067, 0.090, 0.175, 0.195, 0.349, 0.455, 0.667, 0.819, 0.852, 0.961 Take home quiz #20 2. The Venn Diagram at the right shows sports participation for boys enrolled in athletics at a high school. In the Venn diagram, F F = {male athletes who play football}, B={male athletes who play basketball}, and T = {male athletes involved in track & field} 14 %3D 12 8. 10 %3| 9. An athlete is selected at random. Find the following probabilities (write your answer as BOTH a fraction and a decimal rounded to 3 decimal places). 15 16 (a) P(F) (b) P(B') (c) P(BnT') (d) P(T UF) 100beraltald (e) P(T|B) (f) P(F\T°) (g) find the probability an athlete runs track, given that they play football or basketball (or both). (h) find the probability an athlete plays a second sport, given that they play football. (i) find the probability an athlete plays basketball, given that they don't play football or run track (j) find the probability an athlete plays football only, given that they don't play basketball. Che bur answers (not in order) : 0.220, 0.269, 0.32, 0.424, 0.462, 0.487, 0.5. 571, 0.667, 0.725