A bag contains 4 Red and 6 Black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with 3 additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red is

i. Probability that the first ball is black and second is red.
Total number of black balls \(=6\)
Total number of red balls \(=4\)
Probability of getting black ball in first draw \(=\frac{6}{10}\).
Now, number of black balls \(=9\) and Total number of balls = 13
\(\therefore \quad\) Probability of getting red ball in second draw \(=\frac{4}{13}\).
ii. Probability that both the balls are red.
Probability of getting red ball in first draw \(=\frac{4}{10}\).
Now for second draw, -
Number of red balls \(=7\) and
Total number of balls \(=13\).
\(\therefore \quad\) Probability of getting red ball in second draw \(=\frac{7}{13}\)
\(\therefore \quad\) Total probability of drawing red ball
\(\begin{aligned}
& =\left(\frac{6}{10} \times \frac{4}{13}\right)+\left(\frac{4}{10} \times \frac{7}{13}\right) \\
& =\frac{24+28}{130} \\
& =\frac{26}{65}
\end{aligned}\)