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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 ?


Solution


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 = $$\dfrac{5}{9}$$


Maths

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