Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is
Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is
$1 / 2$
$3 / 4$
$3 / 8$
$5 / 16$
Solution
Product of 2 numbers is even if either both are even or
1 is even and 1 odd.
Number of ordered pair: for 1 even and 1 odd
$=($ Selecting 1 odd out of 3 and selecting 1 even out of 3$)$
$\times 2(\mathrm{a}, \mathrm{b})$ and $(\mathrm{b}, \mathrm{a})$ are difference hence multiplied by 2
$=2 \times{ }^3 \mathrm{C}_1 \times{ }^3 \mathrm{C}_1=18$
and both even: $(2,2)(2,4),(2,6)(4,2),(4,4),(4,6)$, $(6,2),(6,4),(6,6)$
Total number of favourable outcome $=18+9=27$
Total outcomes $=36$
Probability $=27 / 36=3 / 4$