Question

A bag of marbles contains 3 blue marbles, 2 green marbles. 2 marbles are selected from the bag without replacement. What is the probability of getting 1 green marble?

Answer 1

A bag of marbles contains 3 blue marbles, and 2 green marbles.

2 marbles are selected from the bag, without replacement.

We have to find the probability of getting 1 green marble.

Now, there are a total of (3+2), ie. 5 marbles.

Now, from this bag, the first marble can be drawn in 5 ways; as the drawings are without replacement, so the second marble can be drawn in 4 ways.

So, all possible cases is

=

Now, we have to have 1 green marble, out of the 2 marbles drawn.

First, we have to choose which drawing out of the 2 has the green marble; this can be done in 2 ways.

Now, for any of these 2 cases, the green marble can be drawn in 2 ways. The other one can not be a green one; so the other draw can have 3 options from 3 blue marbles.

So, the number of favourable cases is

=

Now, we know that the probability of an event is the ratio of the number of favourable cases for the event, to the number of all possible cases.

So, the required probability is

So, the probability of getting a green marble is 0.6.