Question

An urn contains 2 black, 3 red, and 5 green balls. The balls are taken out one after the other 6 times and we are told that one of them is green. What is the probability that none of the other balls are green? Assume that the balls are non-identical in weight even though they have the same color

Answer 1

2 Black

3Red

5 Green balls

Total 10 Balls

From which we need to take 6 balls

Given 1 of the 6 balls is green

Now we need to find  the probability that none of the other balls are green

i.e. remainig 5 balls are to be selected from 2 Black and 3 Red balls that is all of them to be seleted

Total permutations of selecting 5 balls from 10 remaining balls= 10C5 = 252

Total occurrences where we can have no green balls selected = 2C2 * 3C3 = 1

Hence the asked Probability = occurrences/total permutations

=1/252 =0.003968254

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