Question

A number x is selected from the numbers 1, 2, 3 and then a second number y is randomly selected from the numbers 1, 4, 9. What is the probability that the product xy of the two numbers will be less than 9 ?

Answer 1

Number x can be selected in three ways and corresponding to each such way there are three ways of selecting number y. Therefore, two numbers can be selected in 9 ways as listed :

$(1,1),(1,4),(1,9),(2,1),(2,4),(2,9),(3,1),(3,4),(3,9)$

So, total number of elementary events = 9

The product xy will be less than 9, if x, and y are chosen in one of the following ways :

$(1,1),(1,4),(2,1),(2,4),(3,1)$

Therefore, favourable number of elementary events = 5

Therefore, required probability = $\frac{5}{9}$