If you are required to replace the first ball after picking it, the probability of picking a purple ball on the first draw remains the same, which is 1/10 since there are 10 colorful balls total.
However, after replacing the first ball, the total number of balls remains the same at 10, but now there is only 1 purple ball left out of 10, which results in a 1/10 probability of picking a purple ball on the second draw.
Therefore, the probability of winning by picking 2 purple balls in a row when replacing the first ball is (1/10) * (1/10) = 1/100.
Comparing this to the original probability of winning when not required to replace the first ball which was (1/10) * (1/9) = 1/90, you are 10 times less likely to win if you are required to replace the first ball.
there are 10 colorful balls that are the same size and texture. you are required to pick 2 balls. if both of the balls that you pick are purple then you win. how much less likely are you to win if you are required to replace the first ball?
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