Three marbles are chosen without replacement from a box cont

Three marbles are chosen without replacement from a box containing 2 green, 5 red, 6 yellow , and 4 blue marbles. Let X be the number of yellow marbles chosen.

a) Find and graph the probability distribution of X.

b) Find the mean of the random variable X.

Solution

X -- No of yellow marbles chosen

X can take values as 0,1,2,3

X is binomial with two outcomes yellow and non yellow.

For yellow p = 6/17 = 0.3529

q = 0.6471

Thus distribution of Y will be binomial

The prob (y = r) = 3Cr (0.3529)^r(0.6471)^3-r

Mean = np = 3(0.3529)

= 1.0588