There are two bags. Bag I contains 1 red and 3 white balls, and Bag II contains 3 red and 5 white balls. A bag is selected at random and a ball is drawn from it. Find the probability that the ball so drawn is red in colour.

From the given data,
Let assume that A is the event of choosing the Bag I, B is the event of choosing the Bag II and C is the event of drawing a red ball.
Therefore, $\mathrm{P}\left(\mathrm{A}\right)=\mathrm{P}\left(\mathrm{B}\right)=\frac{1}{2}$
Now total balls in Bag I = 1 + 3 = 4
The probability of drawing a red ball from Bag I is,
$\mathrm{P}(\mathrm{C}/\mathrm{A})=\frac{1_{C_1}}{\mathrm{n}-1}=\frac{1}{1}$
Now total balls in Bag II = 3 + 5 = 8
The probability of drawing a red ball from Bag II is,
$\mathrm{P}(\mathrm{C}/\mathrm{B})=\frac{3_{C_1}}{8_{C_1}}=\frac{3}{8}$
Therefore, by doing the sum of P(C|A) and P(C|B) we can find the probability of drawn ball is red.
$\therefore \mathrm{P}\left(\mathrm{C}\right)=\mathrm{P}(\mathrm{C}/\mathrm{B})+\mathrm{P}(\mathrm{C}/\mathrm{B})=\frac{1}{4}+\frac{3}{8}=\frac{5}{8}$
Hence, the probability of drawn selecting the random bag and ball is drawn red is $\frac{5}{8}$.