Question

5% of people sampled a new cola product before it came out. It was found that the people who sampled it were three times as likely to purchase the new cola as those who did not sample it first. A person purchases this new cola. Find the probability that this person sampled it previously. Give your answer to three decimal places.

Answer 1

Event A ----------- Purchasing new cola

Partition B1-----------------Sample people

             B2-----------------Remaining people

A/B1 -----------------A person purchasing cola from sample

A/B2 -----------------A person purchasing cola from Remaining people

P(B1) = 0.05

P(B2) = 0.95

P(A/B1) = 3x

P(A/B2) = x

P(B1/A) = ? probability of partition B1 when Event A is already occured

Using Bayes Theorem:-

P(B1/A) =   

             =

             = 0.05 * 3x / [ 0.05 * 3x + 0.95 * x ]

             = 0.136