One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked …

Question

One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both dice are thrown together, is

Accepted Answer

$\mathrm{a}=$ number or dice 1

$\mathrm{b}=$ number on dice 2

$$(a, b)=(1,3),(3,1),(2,2),(2,3),(3,2),(1,4),(4,1)$$

Required probability

$$\begin{aligned}
& =\frac{2}{6} \times \frac{2}{6}+\frac{1}{6} \times \frac{1}{6}+\frac{2}{6} \times \frac{2}{6}+\frac{2}{6} \times \frac{2}{6}+\frac{1}{6} \times \frac{2}{6}+\frac{2}{6} \times \frac{1}{6}+\frac{1}{6} \times \frac{2}{6} \
& =\frac{18}{36}=\frac{1}{2}
\end{aligned}$$

Solutions · 1