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.

  • $\begingroup$ When you say $\frac{7}{20}$, do you mean $\frac{7}{15}$? $\endgroup$
    – Henry
    Jul 23, 2020 at 8:15
  • $\begingroup$ sorry typo, i have edited it $\endgroup$
    – Ryan Soh
    Jul 23, 2020 at 8:17

2 Answers 2


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.



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?


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