Question

Two marbles are chosen without replacement from a box containing 5 green, 8 red, 5 yellow, and 7 blue marbles. Let X be the number of red marbles chosen. a) Find and graph the probability distribution of X. b) Find E (x)

Answer 1

a)P(x=0)=P(0 red marbles)=P(first not red and second not red)=(20/25)*P(19/24)=19/30

P(X=1)=P(frist red and second not)+P(first not and second is)=(5/25)*(20/24)+(20/25)*(5/24)=1/3

P(X=2)=P(both are red)=(5/25)*(4/24)=1/30

x	P(x)
0	19/30
1	1/3
2	1/30

b)

E(X)= $\sum xP(x)$ =0*(19/30)+1*(1/3)+2*(1/30)=0.4