# Question: question 3 conditional probability an online shop has three types...

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Question 3. Conditional Probability, An on-line shop has three types of customers: regular, casual and occasional buyers, whose probabilities of making a purchase on any given day are 0.7, 0.1 and 0.02, respectively. The proportions of customers in the three categories are 0.25, 0.45 and 0.3 respectively.

Let us define four basic events:

R is the event that a randomly chosen customer of this company is a regular buyer,

C is the event that a randomly chosen customer is a casual buyer,

O is the event that a randomly chosen customer is an occasional buyer,

A is the event that a randomly chosen customer will make a purchase on any given day.

(a) What are the probabilities of the events R, C, O.

(b) In terms of the events R,C,O,A write down the conditional probabilities that a regular, casual or occasional buyer makes a purchase on a given day.

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(c) Determine the probability that an arbitrary customer will make a purchase on a given day.

(d) Determine the probability that a purchase that was made on a particular day was made by a regular customer.