Statistics
posted by Sam .
1.In a jar, suppose there are 3 blue marbles, 2 yellow marbles and one red marble.
c. Suppose that 3 marbles are drawn from the jar without replacement. What is the probability that the 3 marbles are all different colors?
d. Suppose that 4 marbles are drawn from the jar with replacement. What is the probability that exactly 2 of the four drawn are red?
e. Suppose that 3 marbles are drawn from the jar with replacement. How many yellow marbles would you expect to draw?

c) could be RBY RYB YBR YRB BRY OR BYR
prob of each one is (1/6)(3/5)(2/4) = 6/120 = 1/20
the others come out to the same result
so prob (all different) = 6/20 = 3/10
d) prob = C(4,2) (1/6)^2 (5/6)^2
= 6(1/36)(25/36) = 25/216 
c. YOu can do it the following ways:
way Probability
B,Y,R Pr=3/6*2/5*1/4
R,B,Y =1/6*3/5*2/4
B,R,Y =3/6*1/5*2/4
R,Y,B
Y,R,B
Y,B,R
so the probability each time appears to be 3*2*1/6*5*4 so, with six ways, pr must be 6*3*2*1/(6*5*4) and you can reduce that. 
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