Theory question 105
SetsOut 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.
Show the model answer
Model answer
(a) Venn diagram: universal set 120, circles B (bags) and S (shoes) overlapping, intersection 45, nothing outside the circles.
(b) Let n(B) = x, n(S) = x + 11: x + x + 11 − 45 = 120 → 2x = 154 → x = 77
Customers who bought shoes = 88
(c) P(bags) = 77/120
Explanation
n(B ∪ S) = n(B) + n(S) − n(B ∩ S).