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Question 10
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In a class of 200 students, 70 offered Physics, 90 Chemistry, 100 Mathematics while 24 did not offer any of the three subjects. Twenty three (23) students offered Physics and Chemistry, 41 Chemistry and Mathematics while 8 offered all three subjects.
- Draw a Venn diagram to illustrate the information.
- Find the probability that a student selected at random from the class offered:
- Physics only;
- Exactly two of the subjects.
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This question was popular and the candidates did well in it. Though many were able to draw the correct Venn diagram, they could not determine the correct number of students who offered physics and those who offered exactly two of the subjects. Hence, they could not find the required probabilities. They were expected to denote the number of those who offered Physics and Chemistry only by a variable say x, equate the entries to 200 to get 100 + x + 49 – x + 47 – x + 24 = 200, from where x = 20. Number who offered Physics only = 47 – 20 = 27. Therefore probability of those who offered Physics only = 27/200.
Number of those who offered exactly 2 subjects = 15 + 20 + 33 = 68. Probability of those who offered exactly 2 subjects = 68/200 = 17/50
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