Having a box containing 15 red and 7 blue balls. We want to draw 3 balls at random by these conditions on each draw:
- If the ball is red you set it aside
- If the ball is blue put it back in
What is probability that the third draw is blue? (If you get a blue ball it counts as a draw even though you put it back in the box.)
Can I say by these rules?
We have three balls drawn the total possibility is the sum of:
- Both the first two balls are red
- Both the first two balls are blue
- The first ball is red and the second is blue
- The first ball is blue and the second is red.
Then for each case I can calculate the probability of blue ball at third draw.
$ P=\frac{15}{22}*\frac{14}{21}*\frac{7}{20}+\frac{7}{22}*\frac{7}{22}*\frac{7}{22}+\frac{7}{22}*\frac{15}{22}*\frac{7}{21}+\frac{15}{22}*\frac{7}{21}*\frac{7}{21} $