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

Question

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.

e2-e4 · Accepted Answer

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.

drhab · Answer

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?

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

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