An urn contains different colored marbles. the probability of drawing two green marbles from the urn without replacement is 3/20 , and the probability of drawing one green marble is 2/5 .
what is the probability of drawing a second green marble, given that the first marble is green?
3/50
1/2
3/8
1/5

The probability of drawing a second green marble, given that the first marble is green is:

Let A denote the event that first marble is green.

B denote the event that the second marble is green.

A∩B denote the event that both the marbles are green.

Let P denote the probability of an event.

We are asked to find:

                      P(B|A) i.e. probability of drawing a second green marble, given that the first marble is green.

We know that:

Probability of drawing one green marble is 2/5  i.e.

The probability of drawing two green marbles from the urn without replacement is 3/20 i.e.

Hence, we have:

so, converting firstly the mixed fractions to improper fractions and then "adding".