Question

5. Out of 120 customers in a shop, 45 bought both bags and shoes. If all the customers bought either bags or shoes and 11 more customers bought shoes than bags: (a) Illustrate this information in a diagram; (b) Find the number of customers who bought shoes; (c) Calculate the probability that a customer selected at random bought bags.

Accepted Answer

Let n(Bags only)=x, n(both)=45. n(Shoes)=n(Bags)+11. Using a Venn diagram with universal set 120: (x+45)+11+45+x=120 → 2x+101=120... solving via n(S)=n(B)+11 and total = n(B)+n(S)-45=120 (since all bought at least one): with n(S)=x+11, n(B)=x: x+(x+11)-45=120 → 2x-34=120 → 2x=154 → x=77 (number who bought bags). (b) Number who bought shoes = 77+11=88. (c) P(bought bags) = 77/120 ≈ 0.642.

WAEC Mathematics 2017 Theory — Question 8

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