Question

If $x$ is chosen at random from the set $\{1,2,3,4\}$ and $y$ is chosen at random from the set $\{5,6,7\}$, then the probability that $xy$ will be even is

• A. $\dfrac{5}{6}$
• B. $\dfrac{1}{6}$
• C. $\dfrac{1}{2}$
• D. $\dfrac{2}{3}$

Hint:

Odd × Odd = Odd; any even factor makes the product even.

Answer 1

The Correct Option is D

$\{1,2,3,4\}$ has 2 odd (1,3) and 2 even (2,4) numbers.
$\{5,6,7\}$ has 2 odd (5,7) and 1 even (6).
Total pairs = $4 \times 3 = 12$
An even product occurs if either $x$ or $y$ is even.
Only odd $x$ and odd $y$ give odd product.
Number of such pairs = $2 \times 2 = 4$
So, number of even product cases = $12 - 4 = 8$
Required probability = $\dfrac{8}{12} = \dfrac{2}{3}$