Originally Posted by

**jjbrian** A special deck of 50 cards has 5 colors (red, white, blue, purple, and gold); for each color, there are cards numbered 1 through 10. 15 cards are picked at random without replacement from this deck. Let X be the number of purple cards picked. Find E(X) and Var(X).

Heres what I did

The probability distribution is

P(X=0) = C(40,15) / C(50,15) picks the 15 from the 40 that are not purple.

P(X=1) = C(40,14) *C(10,1) / C(50,15) picks 14 from 40 not purple and 1 from 10 purple cards.

P(X=2) = C(40,13) *C(10,2) / C(50,15) picks 13 from 40 not purple and 2 from 10 purple cards.

.

.

.

.

.

P(X=10) = C(40,5) *C(10,10) / C(50,15) picks 5 from 40 not purple and 10 of 10 purple cards.

I used a calculator to find the probability of each.

Using the formula E(X) = sum P(U)*X(U)

I got E(X) to be 3.0

then var(X) =E(x^2)- [E(X)]^2

to get var(x) to be 1.71

Im not sure if the method i used is correct. Please comment..