If C is the original value of the asset, S is the scrap value, n is the useful life of the asset and D is the annual depreciation, then

There are two boxes:

Box 1: 2 black + 4 red = 6 total balls

Box 2: 4 black + 3 red = 7 total balls

A ball is drawn at random from one of the two boxes. This means one box is randomly selected first, then a ball is drawn from that chosen box.

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Probability of selecting Box 1 = $\frac{1}{2}$21​

Probability of getting black from Box 1 = $\frac{2}{6}$62​

Probability of selecting Box 1 and getting black = $\frac{1}{2} \times \frac{2}{6}$21​×62​

$$= \frac{2}{12}$$=122​

$$= \frac{1}{6}$$=61​

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Probability of selecting Box 2 = $\frac{1}{2}$21​

Probability of getting black from Box 2 = $\frac{4}{7}$74​

Probability of selecting Box 2 and getting black = $\frac{1}{2} \times \frac{4}{7}$21​×74​

$$= \frac{4}{14}$$=144​

$$= \frac{2}{7}$$=72​

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Total probability of getting a black ball = $\frac{1}{6} + \frac{2}{7}$61​+72​

LCM of 6 and 7 = 42

$$\frac{1}{6} = \frac{7}{42}$$61​=427​

$$\frac{2}{7} = \frac{12}{42}$$72​=4212​

Total probability = $\frac{7}{42} + \frac{12}{42}$427​+4212​

$$= \frac{19}{42}$$=4219​

Therefore, the probability of getting a black ball is $\frac{19}{42}$4219​.