Three marbles are chosen without replacement from a box cont

Three marbles are chosen without replacement from a box containing 5 red, 8 blue, and 10 yellow marbles. Let X be the number of yellow marbles chosen. Find and graph the probability distribution of X. Find the mean of the random variable X. Please show all work

Solution

a)The probability distribution of X is as follows:

X:          1         2         3

P(X): 9/24        8/23    7/22

Since the three marbles are chosen without replacement this is a normal probability plot.

b)The mean of X is:

E(X)=1*9/24+2*8/23+3*7/22

=0.375+0.695+0.954

=2.024