JEE Main 2018 — Probability Question with Solution

If we follow path 1, then probability of getting 1st ball black $$=\frac{6}{10}$$ and probability of getting 2nd ball red when there is 4 R and 8 B balls = $$\frac{4}{12}$$.

So, the probability of getting 1st ball black and 2nd ball red = $$\frac{6}{10}\times \frac{4}{12}$$.

If we follow path 2, then the probability of getting 1st ball red $$=\frac{4}{10}$$ and probability of getting 2nd ball red when in the bag there is 6 red and 6 black balls = $$\frac{6}{12}$$

$$\therefore$$ Probability of getting 2nd ball as red

$$=\frac{6}{10}\times \frac{4}{12}+\frac{4}{10}\times \frac{6}{12}$$

$$=\frac{1}{5}+\frac{1}{5}$$

$$=\frac{2}{5}$$