Question

If 4 whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, 7 or 9 is

• A. $\frac{16}{625}$
• B. $\frac{4}{125}$
• C. $\frac{8}{81}$
• D. none

Answer 1

The correct option is A $\frac{16}{625}$

Given the product has to end in 1,3,7 or 9.

The units place of all the 4 numbers we want to multiply can't end in 0, 2, 4, 5, 6, 8. That means it can only end in 1, 3, 7, 9.

This means that the probability of selecting 1 number that ends in 1, 3, 7 or 9 is 4/10 = 2/5

$\therefore$ the probability of selecting 4 numbers that end in 1, 3, 7 or 9 is $\frac{2}{5}\times \frac{2}{5}\times \frac{2}{5}\times \frac{2}{5}=\frac{16}{625}$