List of practice Questions

An experiment is performed by rolling an unbiased die once. Events A and B are defined as follows:
Event A: The outcome of the rolled die is a prime number.
Event B: The outcome of the rolled die is an odd number less than 4.
The conditional probability of A given B, denoted by P(A|B), is ______ (rounded off to one decimal place).

A retail shop sells three brands of tea, namely Brand A, Brand B, and Brand C, and each in two varieties, namely regular and premium. The proportion of customers buying the Brands A, B, and C are \(40\%\), \(35\%\), and \(25\%\), respectively. Out of those customers who buy Brand A, \(30\%\) buy the premium variety, out of those who buy Brand B, \(40\%\) buy the premium variety, while out of those who buy Brand C, \(60\%\) buy the premium variety. Given that a randomly selected customer has bought the premium variety of tea, the probability that he/she has bought Brand B equals