There are 2 pots. One pot has 5 red and 3 green marbles. Other has 4 red and 2 green marbles. What is the probability of drawing a red marble?

Answer: Option B

Here, one probability is to find which pot is selected and other is for red marble from the selected pot,
Probability of selecting 1 post out of 2 pots = $$\frac{1}{2}$$
Say it has 4 red and 2 green marbles
So, Red marble probability = $$\frac{4}{4+2}$$ = $$\frac{4}{6}$$
So Probability 1 $$=\frac{1}{2}\times \frac{4}{6}=\frac{4}{12}$$
Similarly, Probability 2 $$=\frac{1}{2}\times \frac{5}{5+3}=\frac{5}{16}$$
Total probability of red ball
$$\begin{array}{rl}& =\frac{4}{12}+\frac{5}{16}\\ & =\frac{31}{48}\end{array}$$