Question

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

• A. $\frac { 369 } { 625 }$
• B. $\frac { 399 } { 625 }$
• C. $\frac { 123 } { 625 }$
• D. $\frac { 133 } { 625 }$

Answer 1

Answer: (A)

$\frac { 369 } { 625 }$

Answer 2

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 one of the ten digits 0, 1, 2,…, 9. So, the total number of ways of selecting last digits of four numbers is 10 × 10 × 10 × 10 = 10⁴. 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 = 8⁴. Therefore, the probability that the product is not divisible by 5 or 10 is$\left( \frac { 8 } { 10 } \right) ^ { 4 }$. Hence, required probability = 1 – $\left( \frac { 8 } { 10 } \right) ^ { 4 }$ = $\frac { 369 } { 625 }$ .

Hence, (1) is correct answer