Question

Two dice are thrown simultaneously. The probability of getting a multiple of $2$ on one die and a multiple of $3$ on the other is ___________.

• A. $\frac{5}{36}$
• B. $\frac{5}{12}$
• C. $\frac{11}{36}$
• D. $\frac{1}{12}$

Answer 1

Answer: (C)

$\frac{11}{36}$

The required probability $=\frac{3}{6}$ (multiple of $2$ on one dice) $\times \frac{2}{6}$(multiple of $3$ on the other dice) $+\frac{2}{6}$ (multiple of $3$ on one dice) $\times \frac{3}{6}$ (multiple of $2$ on other dice) $-\frac{1}{6}$ (case both dice having $6$, is repeated both times)

$=\frac{6}{36}+\frac{6}{36}-\frac{1}{6}$

$=\frac{11}{36}$