A box contains 2 black and 4 red balls and another box contains 4 black and 3 red balls. If a ball drawn at random from one of the two boxes, then the probability of getting a black ball is

$\frac{19}{42}$

The correct answer is Option (3) → $\frac{19}{42}$

Total boxes = 2

Probability of choosing either box = $\frac{1}{2}$

Box 1: 2 black, 4 red ⇒ total = 6

Probability of black from Box 1 = $\frac{2}{6} = \frac{1}{3}$

Box 2: 4 black, 3 red ⇒ total = 7

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

Total probability of drawing a black ball:

$= \frac{1}{2} \cdot \frac{1}{3} + \frac{1}{2} \cdot \frac{4}{7}$

$= \frac{1}{6} + \frac{2}{7} = \frac{7 + 12}{42} = \frac{19}{42}$