Probability of choosing colored balls

Hi, I had a problem in class that goes like this
There's a bag with 3 red balls and 2 blue balls. You choose randomly 2 balls out of the bag. What's the probability distribution function for the number of red balls?

Given X =x corresponds to the number of red balls chosen when you choose 2 balls out of the bag.
What are the probabilities of X= 0, X =1, X=2? In other words, what are the probabilities of choosing 0 , 1 , 2 red balls when you choose 2 balls out of the bag?

Is there anyway to solve this as a Conditional Probability?
Can I interpret it as the probability of choosing x red balls (0 to 2) given that you're choosing 2 balls?

Thanks a lot!

G3rmini1412 said:

There's a bag with 3 red balls and 2 blue balls. You choose randomly 2 balls out of the bag. What's the probability distribution function for the number of red balls?
Given X =x corresponds to the number of red balls chosen when you choose 2 balls out of the bag.
What are the probabilities of X= 0, X =1, X=2?

Click to expand...

Think of \(\displaystyle (B_1B_2)+(B_1R_2+R_1B_2)+(R_1R_2)\)

So \(\displaystyle \begin{array}{*{20}{c}}X&|&0&1&2\\\hline{P(X)}&|&{\frac{2}{{20}}}&{\frac{{12}}{{20}}}&{\frac{6}{{20}}}\end{array}\)

Please reply showing your own work.