Question

Four numbers are multiplied together. Then the probability that the product will be divisible by 5 or 10 is:

• A. $\frac{169}{625}$
• B. $\frac{369}{625}$
• C. $\frac{169}{1626}$
• D. $noneofthese$

Answer 1

The correct option is B $\frac{369}{625}$

The divisibility of the product of four numbers depends upon the value of the last digit of each number. The last digit of a number can be any of the 10 digits 0,1,2,...9. So, the total number of ways of selecting last digits of four numbers is $10\times 10\times 10\times 10={10}^4$.
If the product of the 4 numbers is not divisible by 5 or 10.
Then the number of choices for the last digit of each number is 8 (excluding 0 or 5).
So, favourable number of ways = $8\times 8\times 8\times 8=8^4$
$\therefore$ The probability that the product is not divisible by 5 or 10
$=\frac{8^4}{{10}^4}={\left(\frac{8}{10}\right)}^4$
Hence, Required probability = $1-{\left(\frac{8}{10}\right)}^4=\frac{369}{625}$