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.
Best 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.