Really could use some math help?

A drawer contains 12 socks. There are 6 different colors of socks with 2 socks of each color. you are going to pick a sample of 4 socks without replacement. blue happens to be your favorite color. the random variable is the number of blue socks in the sample chosen.





a) give the value(s) that the random variable can take on.


b) give the probability of distribution for the random variable


c) give the expected value of the random variable


d) what is the probability that there will be at least one blue sock in the sample?





thanks soo much, we have been boggling our minds for a couple hours now and to no avail

Really could use some math help?
a) 0, 1, 2





b) P(0) = (10/12)*(9/11)*(8/10)*(7/9) = (7*8)/(11*12) = .4242


P(2) = (2/12)*(1/12) = 1/72 = .0139





P(1) = 1-P(0)-P(2) = 1-.4242-.0139= .5619





c) Expected value = 0 *(.4242) + 1*(.5619) + 2*(.0139) = .5897





d) P(At least 1 blue sock) = P(1) + P(2) = .5619+.0139 = .5758
Reply:a . 2/12=1/6


b. 2/12=1/6


c. 2/12=1/6


d. 1/6*1/6*1/6*1/6=1/1296 (since you are picking 4 socks without replacing them, you have a 1/6 chance of picking one blue with every pick)