Probability - Venn

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Probability - Basic Venn diagrams.
Test Yourself 1.

	1. In a class of 30 students, 25 study Mathematics and 20 study Physics. If a student is chosen at random from this class, determine the probability that: (i) the student studies both Mathematics and Physics. (ii) The student studies Mathematics but not Physics. Answer.(i) 15/30 = 0.5. (ii) 10/30 = 0.33.
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	3. In a class of 30 students, students at least one of the subjects Ancient History and Modern History. There are 16 students studying Ancient History and 20 students studying Modern History. (i) How many students study both History subjects? (ii) A student is chosen at random from the group. What is the probability that student studies Modern History but not Ancient History? (iii) Two students are selected at random from the group. What is the probability that both students study Ancient History? Answer.(i) 6 students study both. (ii) Pr(Modern) = 7/15. (iii) Pr (both ancient students!!) = 3/29.
	4. There are 35 patients in a hospital casualty room with broken bones, a sports injury of both. Of the patients waiting, 25 have a broken bone, 15 have a sports injury. A patient is selected at random. What is the probability that the patient has a sports injury but not a broken bone? Answer.Pr (sports injury) = 5/7.
	5. In a class of 28 students, there are 19 who like Geometry and 16 who like Trigonometry. Although impossible to believe, 45 students claim to like neither. By drawing a Venn diagram, determine the probability that a student chosen at random from this class will like only trigonometry. Answer.Prob Trig only = 1/7.
	6. Eighteen people attend a Collectors meeting. Of these, 14 people collect stamps and 10 collect coins. A person is selected at random. What is the probability that the selected person does not collect coins? Answer.Pr (not coins) = 4/9.
	7. In a small town outside of Glasgow in Scotland, 800 people are direct descendents of the Johnstone clan while 500 are direct descendents of the Johnson clan. There are 3,200 people living in that town and 1200 are descendants of neither the Johnstone nor the Johnson clans (so maybe the Campbells?). If one of the towns residents is chosen at random, what is the probability that person has both Johnstone and Johnson ancestry. Answer.Pr (both clans) = 5/32.
	8. At an athletics carnival, 36 Year 12 students attend. Of these, 28 students enter running events and 20 students enter field events. A student is selected at random from the 36 students. What is the probability that the selected student has not entered a running event? Answer.Pr (not running) = 16/36 = 4/9.
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