SOLUTION: 100 red gumball 100 green gumballs a penny gets you 6 gumballs what is the chance of getting all 6 green gumballs

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Question 552589: 100 red gumball 100 green gumballs a penny gets you 6 gumballs what is the chance of getting all 6 green gumballs
Answer by AnlytcPhil(1808) About Me  (Show Source):
You can put this solution on YOUR website!
C(100,6)
-------- = .014465141
C(200,6)

Or you can look at it this way.  Suppose the gumballs come out one at a time.

The probability that the 1st one is green is 100%2F200 = 1%2F2
The probability that the 2nd one is green is 99%2F199 
The probability that the 3rd one is green is 98%2F198 = 49%2F99
The probability that the 4th one is green is 97%2F197 
The probability that the 5th one is green is 96%2F196 = 24%2F49
The probability that the 6th one is green is 95%2F195 = 19%2F39

Desired probability 
            
1%2F299%2F19949%2F9997%2F19724%2F4919%2F39 =

           4
          cross%288%29
1%2Fcross%282%29cross%2899%29%2F199cross%2849%29%2Fcross%2899%2997%2F197cross%2824%29%2Fcross%2849%2919%2Fcross%2839%29 = %2897%2A4%2A19%29%2F%28199%2A197%2A13%29 = 7372%2F509639 = .014465141 
            13





Edwin