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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.

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  • $\begingroup$ 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

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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.

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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?

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