There is a large container, which holds the following. 10 balls, 2 purple, 1 yellow, 2 orange, 2 green, 1 blue, 2 red. The balls are the same size and texture. You are required to select two balls. If both the balls that you select are purple, then you went 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.
First, let's find the probability of selecting two purple balls without replacement.
The probability of selecting the first purple ball is 2/10.
Once we have selected one purple ball, there will be 9 balls left, with 1 purple ball remaining out of those 9 balls. So the probability of selecting the second purple ball is 1/9.
Therefore, the probability of selecting two purple balls without replacement is: (2/10) * (1/9) = 2/90 = 1/45
Now, let's find the probability of selecting two purple balls with replacement.
The probability of selecting the first purple ball is 2/10.
Since we are replacing the ball, the probability of selecting the second purple ball is still 2/10.
Therefore, the probability of selecting two purple balls with replacement is: (2/10) * (2/10) = 4/100 = 1/25
To find how much less likely you are to win if you are required to replace the first ball, we can compare the two probabilities:
1/25 - 1/45 = (9/225) - (5/225) = 4/225
Therefore, you are 4/225 less likely to win if you are required to replace the first ball.