There is a large container which will hold the following: 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.

Answer 1

When you select the first ball, there is a 1 out of 4 chance that it will be purple, as there are 4 balls in total and one of them is purple.

If you replace the first ball before selecting the second ball, the probability of selecting a purple ball on the second draw remains 1 out of 4. This is because each ball has an equal chance of being selected each time, regardless of whether or not the first ball was replaced.

To calculate the combined probability of both events happening (selecting a purple ball on the first draw and a purple ball on the second draw), you multiply the individual probabilities:

1/4 (probability of selecting a purple ball on the first draw) x 1/4 (probability of selecting a purple ball on the second draw) = 1/16

So, the probability of winning if you are required to replace the first ball is 1 out of 16, compared to 1 out of 4 if you are not required to replace the first ball. Therefore, you are 4 times less likely to win if you are required to replace the first ball.