Question

If $4$ whole numbers taken at random are multiplied together show that the chance that the last digit in the product is $1,3,7$, or $9$ is $\frac{16}{625}$.

Answer 1

If the last digit is $1,3,7,9$ in the product then we can only select numbers whose last digit is $1,3,7$ or $9$ from $0,1,2,.....9$

Probability that a selected number ends with $1,3,7$ or $9$ $=\frac{4}{10}=\frac{2}{5}$

Probability of selecting four such numbers $={\left(\frac{2}{5}\right)}^4=\frac{16}{625}$

Hence proved.