Read a three-set Venn diagram and calculate exact-two, only-one and neither probabilities.
Read a three-set Venn diagram and calculate exact-two, only-one and neither probabilities.
6 marks
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The Venn diagram below shows information about \(120\) students in a school. Of these, \(40\) study Chinese (C), \(35\) study Japanese (J), and \(30\) study Spanish (S). A student is chosen at random from the group. Find the probability that the student
- studies exactly two of these languages;[1]
- studies only Japanese;[2]
- does not study any of these languages.[3]
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Answer:(a) \(\frac{19}{120}\)
(b) \(\frac{1}{8}\)
(c) \(\frac{11}{30}\)
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