Question

What is the probability that product of two integers chosen at random has the same unit’s digit as the integers themselves?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

An integer can end with any of the ten’s digits (0, 1, 2 ... 9) out of which if it ends with one of the four (0, 1, 5, 6), the required condition will be satisfied. The probability of an integer ending with 0 or 1 or 5 or 6 is $\frac{4}{10}$ = $\frac{2}{5}$ Now the probability of second integer also ending with the digit that has come in the unit’s place of the first integer is $\frac{1}{10}$

Therefore, the required probability = $\left(\frac{2}{3}\right)$ $\times$ $\left(\frac{1}{10}\right)$ = $\frac{1}{25}$