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TOPIC 14

Learn how to use Venn diagrams to solve probability questions with two examples. Understand the probability of playing snooker, playing both chess and snooker, and playing neither chess nor snooker. Discover the probability of being left-handed given that a student wears glasses, and the probability of a left-handed student also wearing glasses.

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TOPIC 14

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  1. TOPIC 14 Venn Diagrams

  2. Venn Diagrams Another approach to answering PROBABILITY questions is to use a VENN DIAGRAM. Example 1 Draw a Venn diagram to show the following information. In a group of 30 students, 15 play chess, 10 play snooker and 6 play both. Use your diagram to find: • The probability that a student chosen at random from the group plays snooker. • The probability that the student plays both chess and snooker. • The probability that the student plays neither chess nor snooker.

  3. Venn Diagrams S C Answer 1 • P(S) = 10 = 1 30 3 • P(C and S) = 6 = 1 30 5 • P(neither) = 11 30 9 4 6 11

  4. Venn Diagrams Example 2 In a school sixth form 12% of the students are left-handed, 15% of the students wear glasses, and 3% are both left handed and wear glasses. • Given that a student wears glasses, find the probability that they are left-handed. • What is the probability that a left-handed student also wears glasses?

  5. Venn Diagrams G L Answer 2 • P(L|G) = 3 = 1 15 5 • P(G|L) = 3 = 1 12 4 9% 12% 3% 76%

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