Question

The probability that two integers chosen at random and their product will have the same last digit is:

• A. $\frac{3}{10}$
• B. $\frac{1}{25}$
• C. $\frac{4}{15}$
• D. $\frac{7}{15}$

Answer 1

The correct option is B $\frac{1}{25}$

The condition implies that the last digit in both the integers should be 0, 1, 5 or 6 and the probability
$=4{\left(\frac{1}{10}\right)}^2=\frac{4}{100}=\frac{1}{25}$
[$\therefore$ The squares of numbers ending in 0 or 1 or 5 or 6 also end with 0 or 1 or 5 or 6 respectively]