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 the 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.
Explanation
(a)
(b) (x + 45 + x + 11 = 120 implies 2x + 56 = 120)
(2x = 120 – 56 = 64)
(x = 32)
Therefore, the number of customers that bought bags = 32.
(c) (P(text{a random customer bought bags}) = frac{text{no of customers that bought bags}}{text{total no of customers}})
No of customers that bought bags = 32 + 45 = 77
(P(text{customer bought bag}) = frac{77}{120}).