Question

If any four numbers are selected and they are multiplied then the probability that last digit in the product will be $1,3,5\mathrm{or}7$ is

• A. $\frac{4}{625}$
• B. $\frac{18}{625}$
• C. $\frac{16}{625}$
• D. none of these

Answer 1

The correct option is C

$\frac{16}{625}$

Finding the probability:

Given, Total outcome is $\left\{0,1,2,3,4,5,6,7,8,9\right\}=10$.

Favorable outcome, Last digit with $1,3,5\mathrm{or}7$ is $4$.

The probability that of selected a number ends with $1,3,5\mathrm{or}7$ is $=\frac{4}{10}=\frac{2}{5}\frac{\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{f}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{O}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{O}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}$

Required probability that of selected four number ends with $1,3,5\mathrm{or}7$ is ${\left(\frac{2}{5}\right)}^4=\frac{16}{625}$

Hence, correct answer is option $\left(C\right)$