SOLUTION: A drawer contains four red socks and two blue socks. Three socks are drawn from the drawer without replacement. (a) Create a probability distribution in which the random variable

Algebra ->  Probability-and-statistics -> SOLUTION: A drawer contains four red socks and two blue socks. Three socks are drawn from the drawer without replacement. (a) Create a probability distribution in which the random variable      Log On


   

Question 1142074: A drawer contains four red socks and two blue socks. Three
socks are drawn from the drawer without replacement.
(a) Create a probability distribution in which the random variable repre-
sents the number of red socks.
(b) Determine the expected number of red socks if three are drawn from
the drawer without replacement.
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


(a) probability distribution....

P%283%29+=+%28C%284%2C3%29%2AC%282%2C0%29%29%2FC%286%2C3%29 (choose 3 of the 4 red socks and 0 of the 2 blue socks)

P%282%29+=+%28C%284%2C2%29%2AC%282%2C1%29%29%2FC%286%2C3%29 (choose 2 and 1)

P%281%29+=+%28C%284%2C1%29%2AC%282%2C2%29%29%2FC%286%2C3%29 (choose 1 and 2)

P(0) = 0, because there are not 3 blue socks.

As a check on your calculations, verify that the sum of all the probabilities is 1.

(b) expected value....

3%2AP%283%29%2B2%2AP%282%29%2B1%2AP%281%29%2B0%2AP%280%29