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

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Solution

Q.
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 [2025]

1 $\frac{1}{2}$

2 $\frac{2}{3}$

3 $\frac{4}{9}$

4 $\frac{3}{5}$

Ans.
(1)

Let x be the number shows on dice –1 and y be the number shows on dice –2.

Favorable outcomes = {(x, y) = (1, 3), (3, 1), (2, 2), (2, 3), (3, 2), (1, 4), (4, 1)}

$∴$ Required probability

$= \frac{2}{6} \times \frac{2}{6} + \frac{1}{6} \times \frac{1}{6} + \frac{2}{6} \times \frac{2}{6} + \frac{2}{6} \times \frac{2}{6} + \frac{1}{6} \times \frac{2}{6} + \frac{2}{6} \times \frac{1}{6} + \frac{1}{6} \times \frac{1}{6}$

$= \frac{18}{36} = \frac{1}{2}$ .

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