Question

If x is chosen at random from the set $\{2,3,4,5,6\}$, and y is chosen at random from the set $\{11,13,15\}$, find the probability that $xy$ is even.

• A. $\frac{3}{5}$
• B. $\frac{2}{5}$
• C. $\frac{4}{5}$
• D. $\frac{1}{2}$
• E. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{3}{5}$

There are $15$ possible values of $xy$.
i.e: $2\times 11=22$
$2\times 13=26$
$2\times 15=30$
$3\times 11=33$
$3\times 13=39$
$3\times 15=45$
$4\times 11=44$
$4\times 13=52$
$4\times 15=60$
$5\times 11=55$
$5\times 13=65$
$5\times 15=75$
$6\times 11=66$
$6\times 13=78$
$6\times 15=90$
As you see $9$ of these values are even.
So, that the probability that $xy$ is even is $\frac{9}{15}=\frac{3}{5}$ or $0.6$.
Hence, option A is correct.