Two dice are rolled together. Find the probability of getting: (i) a multiple of 2 on one and a multiple of 3 on the other die. (ii) the product of…

Total outcomes = $\displaystyle 36$

$\displaystyle (2, 3)$, $\displaystyle (2, 6)$, $\displaystyle (3, 2)$, $\displaystyle (3, 4)$, $\displaystyle (3, 6)$, $\displaystyle (4, 3)$, $\displaystyle (4, 6)$, $\displaystyle (6, 2)$, $\displaystyle (6, 3)$, $\displaystyle (6, 4)$, $\displaystyle (6, 6)$

Number of outcomes having multiple of $\displaystyle 2$ on one die and a multiple of $\displaystyle 3$ on other die = $\displaystyle 11$

Hence, \(\displaystyle \mathrm{P}(\mathrm{E})=\frac{11}{36}\)

$\displaystyle (1, 1)$, $\displaystyle (2, 2)$, $\displaystyle (3, 3)$, $\displaystyle (1, 4)$, $\displaystyle (4, 1)$, $\displaystyle (4, 4)$, $\displaystyle (5, 5)$, $\displaystyle (6, 6)$

Number of outcomes having product of two numbers on the top of the dice is a perfect square number = $\displaystyle 8$

\(\displaystyle \mathrm{P}(\mathrm{E})=\frac{8}{36}\) or \(\displaystyle \frac{2}{9}\)