# Statistics

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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?

• Statistics - ,

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

• Statistics - ,

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.

• Statistics - ,

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