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?

Solution(By Examveda Team)

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
$$\eqalign{ & = \frac{4}{{12}} + \frac{5}{{16}} \cr & = \frac{{31}}{{48}} \cr} $$