If the number $x$ is chosen from the numbers $1, 2, 3$ and a number $y$ is selected from the number $1, 4, 9$ , find the probability that $x y < 9$ .

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Solution

Number 'x' can be selected in three ways and corresponding to each such way there are three ways of selecting number y therefore, the two numbers can be selected in 9 ways as listed below:
(1,1),(1,4),(1,9),(2,1),(2,4),(2,9),(3,1),(3,4),(3,9)
Total number of outcomes $= 9$
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)
Number of favorable outcomes $= 5$
P(product less than 9) $= \frac{5}{9}$

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If the number x is chosen from the numbers 1,2,3 and a number y is selected from the number 1,4,9, find the probability that xy<9.

If the number $x$ is chosen from the numbers $1, 2, 3$ and a number $y$ is selected from the number $1, 4, 9$ , find the probability that $x y < 9$ .