# Probability question about picking $2$ types of balls out of $3$

I need help with this question:

A bag contains $$2$$ red balls, $$6$$ blue balls and $$7$$ green balls. Victoria draws $$2$$ balls out of the bag. What is the probability that she gets a red ball and a blue ball?

I can figure out the probability of picking $$1$$ ball ($$\frac{2}{15}$$,$$\frac{2}{5}$$,$$\frac{7}{15}$$ respectively). But I am stuck a finding out the probability of 2.

Any help would be appreciated.

• When you say $\frac{7}{20}$, do you mean $\frac{7}{15}$? – Henry Jul 23 at 8:15
• sorry typo, i have edited it – Ryan Soh Jul 23 at 8:17

Your probabilities are correct to draw one ball.

To draw two balls $$B_1$$ and $$B_2$$, you multiply the probability of drawing $$B_1$$ with the probability of drawing $$B_2$$ after drawing $$B_1$$ (only $$14$$ balls are remaining).

Then, how many ways can you draw a red and a blue ball? You can draw a red first, and then a blue, and you can also draw a blue first, then a red.

So you have to calculate both probabilities (red,blue) and (blue,red) and sum them. This is your result.

Guide:

Draw the balls one by one and find the probabilities on BR and RB respectively. Then take the sum.

Concerning e.g. RB: if at first draw a red ball is taken out then what is the probability of drawing a blue ball at second draw?