標題:
Elementary Statistics
發問:
An bag contains 13 blue papers, 23 yellow papers ,13 red papers and 51 green papers. Papers are randomly selected one by one from the bag until three green papers are drawn. Find the probability that exactly ten papers have to be selected in this process.
最佳解答:
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To satisfy this condition, it must be: For the first 9 papers, there are exactly 2 green papers, then: The 10th paper drawn is green. So for the first 9 papers drawn, when selected from 13 + 23 + 13 + 51 = 100 papers in which 51 are green, the probability that there will be exactly 2 green papers will be: 9C2 x (49 x 48 x 47 x 46 x 45 x 44 x 43) x (51 x 50)/(100 x 99 x 98 x 97 x 96 x 95 x 94 x 93 x 92) = 0.05758 Then when the 10th paper is drawn, there are 91 papers in total in which 49 are green. So the required probability is 0.05758 x 49/91 = 0.03100
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