# maths

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urn contains 4 white and 6 red rolls. Four balls are drawn at random (without replacement) from the urn. Find the probability distribution of number of white balls?

• maths -

prob(white) = 4/10 = 2/5, prob(red) = 6/10 = 3/5

no white balls --- (3/5)^4 = 81/625
one white ball -- C(4,1) (2/5) (3/5)^3 = 216/625
two white balls -- C(4,2) (2/5)^2 (3/5)^2 = 216/625
three white balls -- C(4,3) (2/5)^3 (3/5) = 96/625
four white balls -- (2/5)^4 = 16/625

notice that the sum of these is 1 , as it should be

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