Question

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

Answer 1

Calculate probability of the event based on given information

Given :

$x$ is chosen from the numbers $1,2,3$ and a number $y$ is selected from the numbers $1,4,9$ .

Here , $x$ can be chosen in $3$ ways and in accordance with that there are $3$ ways of choosing number $y$, then the possible outcomes are:
$(1,1),(1,4),(1,9),(2,1),(2,4),(2,9),(3,1),(3,4),(3,9)$
Total number of outcomes $\left(S\right)=9$

Now,
The outcomes of given condition $xy<9$, are :
$(1,1),(1,4),(2,1),(2,4),(3,1)$
Number of favourable outcomes $\left(E\right)=5$

Now,
$$\begin{gathered} P\left(xy<9\right)=\frac{Numberoffavourableoutcomes}{Totalnumberofoutcomes} \\ P\left(xy<9\right)=\frac{5}{9} \end{gathered}$$

Hence , If the number $x$ is chosen from the numbers $1,2,3$ and a number $y$ is selected from the numbers $1,4,9$ then the probability that $xy<9$ is $\frac{5}{9}$.