JEE MAIN - Mathematics (2025 - 23rd January Morning Shift - No. 7)
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 the dice are thrown together, is
$\frac{2}{3}$
$\frac{3}{5}$
$\frac{4}{9}$
$\frac{1}{2}$
Explanation
$\mathrm{a}=$ 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
$$\begin{aligned} & =\frac{2}{6} \times \frac{2}{6}+\frac{1}{6} \times \frac{1}{6}+\frac{2}{6} \times \frac{2}{6}+\frac{2}{6} \times \frac{2}{6}+\frac{1}{6} \times \frac{2}{6}+\frac{2}{6} \times \frac{1}{6}+\frac{1}{6} \times \frac{2}{6} \\ & =\frac{18}{36}=\frac{1}{2} \end{aligned}$$
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