If we have to replace the first ball that we picked, the probability of selecting a purple ball on the first try is 1/3, because there are a total of 3 balls and only 1 of them is purple.
After replacing the first ball, the total number of balls remain the same and there is still only 1 purple ball out of 3. So the probability of selecting a purple ball on the second try is also 1/3.
To find the probability of both events happening (selecting a purple ball on the first try and then on the second try), we multiply the probabilities together:
(1/3) * (1/3) = 1/9
Therefore, the probability of winning if we have to replace the first ball is 1/9 or approximately 11.11%.
Comparing this to the situation where we do not have to replace the first ball, the probability of winning is 1/3 or approximately 33.33%.
So we are about 22.22% less likely to win if we have to replace the first ball.
The balls are all the same size and texture. You are required to select two balls.
If both of the balls that you select are purple then you win.
How much less likely are you to win if you are required to replace the first ball? Show all of your work and explain your steps.
1 answer