There are 5 yellow, 4 green, and 2 blue marbles in a hat. You pick 2 marbles from the hat. Marbles are not returned after they have been...

In this question we need to find the probability that the
first marble picked and the second marble picked are
blue.

The probability of this happening is the product of
the probability of the first marble being blue multiplied by the probability of the
second marble being blue.

Lets consider the case where the
first marble is being picked: Here the total number of marbles is 5+4+2=11. The number
of blue marbles is 2. Therefore the probability that the marble being picked is blue is
2/11.

Now we move to the case where the second marble is
being picked. As one blue marble was already picked in the first case, the total number
of marbles is 5+4+1=10 and there is one blue marble. Therefore the probability that a
blue marble is picked is 1/10.

Now taking the product of
the two probabilities we get: (2/11)*(1/10)=
2/110=1/55.

Therefore the probability that
the first marble and the second marble are blue is
1/55.