125 sports fans were interviewed and asked what types of sport they have been to in the last year from a choice of soccer (S), rugby (R) or baseball (B). The following information was obtained. 74 had been to soccer 36 had been to rugby 66 had been to baseball 20 had been to soccer and rugby 27 had been to soccer and baseball 24 had been to rugby and baseball 15 had been to all three types of sport (a) Draw a Venn diagram to show the above information. (b) Find the number of sports fans who, in the last year, had been to (i) baseball only; (ii) both rugby and baseball but not by soccer; (iii) at least two types of sport; (iv) none of the three types of sport. A sports fan is selected at random from those who were interviewed. (c) Find the probability that the sports fan had been to only one type of sport in the last year. (d) Given that the sports fan had been to only one type of sport in the last year, find the probability that the sports fan had been to rugby.

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