If a marble is picked at random and it is green, what is the probability that it is a large one:
In a box there are 60 small and 40 large marbles. 20 of the small marbles are green and the rest are blue. 10 of the large marbles are green and the rest are blue.
In the box there are 100 marbles in all, 60 small and 40 large. Of the small marbles, 20 are green and 40 are blue. Of the large marbles 10 are green and 30 are blue.
When a marble is picked at random from the box it is found to be green. Of the 30 green marbles in the box, 20 are small and 10 are large. This gives the probability that the marble is large as 10/30 = 1/3.
If a green marble is picked from the box there is a probability of 1/3 that it is a large marble.
According to the problem, there are 20 small green marbles, 40 small blue marbles, 10 large green marbles and 30 large blue marbles.
The condition given in the question is that you chose green marble, which there are 30 of them. Ou tof 30 green marbles, 10 are large marbles.
Threfore, you have 10/30 (=1/3) probability of choosing a large marble when it is green one.