An urn contains 4 white and 3 red balls. Let X be the number of red balls in a random draw of three balls. Find the mean and variance of X.

Explanation

There are 4 cases here.

`Case 1:` When no red ball is drawn. All drawn balls are white.Then,

`P(X=0) = (C(4,3)**C(3,0))/(C(7,3)) = (4**1)/((7**6**5)/(3**2**1)) = 4/35`

`Case 2:` When one red ball is drawn. Other two drawn balls are white.Then,

`P(X=1) = (C(4,2)**C(3,1))/(C(7,3)) = (6**3)/35 = 18/35`

`Case 3:` When two red balls are drawn.Third ball is white.Then,

`P(X=2) = (C(4,1)**C(3,2))/(C(7,3)) = (4**3)/35 = 12/35`

`Case 4:` When no white ball is drawn. All drawn balls are red.Then,

...