Question

Assume you are a shopkeeper serving exactly two types of customers:  Type A, who have a 1% probability of purchasing a product upon visiting a store  Type B, who have a 10% probability of purchasing a product upon visiting a store

1. Assume each customer type is equally common. A customer walks into your store and purchases a product. What’s the probability that this customer is of Type A, given that they purchased a product?

2. How would the probability you found in question 1 change if more customers were of Type A? Pick one of the choices below, and write a sentence or two in plain English (i.e. sentences without math) explain your choice

I. Increase

II. Decrease

III. Stay the same

IV. Cannot be determined from the information given

Answer 1

Ans:

P(purchase/type A)=0.01

P(purchase/type B)=0.1

1)P(type A)=P(type B)=0.5

P(purchase)=P(purchase/type A)*P(type A)+P(purchase/type B)*P(type B)

=0.01*0.5+0.1*0.5=0.055

P(type A/purchase)=P(purchase/type A)*P(type A)/P(purchase)

=0.01*0.5/0.055=0.091

2)option I is correct(Increase)