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?

1 answer

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.