SOLUTION: Suppose a jar contains 18 red marbles and 30 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

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Question 1203755: Suppose a jar contains 18 red marbles and 30 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


This problem can be thought of as drawing one marble and then a 2nd marble, without replacement:



P(first is red) = 18/(18+30) = 18/48

P(2nd is red) = 17/(17+30) = 17/47



P(both are red) = (18/48)*(17/47) = 306/2256 or approx. 0.1356 (13.6%)



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If you compute it assuming both are drawn at the same time, you get:

  C(18,2) / C(48,2) = ((18*17)/2) / ((48*47)/2) = (18*17)/ (48*47) = 306/2256, as above.



Where C(n,r) = n!/((n-r)!r!)