1. An automobile dealer has kept records on the customers who visited his showro
ID: 2929970 • Letter: 1
Question
1. An automobile dealer has kept records on the customers who visited his showroom. Sixty percent of the people who visted his dalershsp were fmale. Furthermore, his records show that 40% ofthe females who visited his dealership purchased an automobile, while 20% ofthe males who visited his dealership purchased an automobile. Let A-the event that the customer is female A the event that the customer is male a· Create the Baye's theorem table (label the column appropriately) including formula. b. What is the probability that a customer entering the showroom will buy an automobile? A car salesperson has just informed us that he sold a car to a customer. What is the probability that the customer was female? c.Explanation / Answer
(a)
Purchased Not purchased Total
Male 0.08 0.32 0.40
Female 0.24 0.36 0.60
Total 0.32 0.68 1.00
EXPLANATION:
Given: 60% Female. So, Female total = 0.60. So, male total = 0.40.
Given: 40% femals purchased. So, P(purchaed & female) = 0.60 X 0.40 = 0.24
Given: 20% of males purchased. So, P(Purchased & Male) = 0.40 X 0.20 = 0.08
(b) P(Purchased) = 0.32
(c) P(Female/Purchased) = P(Female & Purchased)/P(Purchased)
= 0.24/0.32 = 0.75
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