4. (15 points total) (a) (5 points) A box contains 5 marbles, 3 Red, 1 Green, 1

Question

4. (15 points total) (a) (5 points) A box contains 5 marbles, 3 Red, 1 Green, 1 Blue. Consider an experiment that consists of taking 1 marble from the box, then replacing it in the box and drawing a second marble from the box. Describe the sample space. repeat when the second marble is drawn without first replacing the first marble. (b) (5 points) What is the probability that the first marble was Green and the second was Blue with replacement? (c) (5 points) What is the probability that the first marble was Green and the sccond was Blue without replacement?

Explanation / Answer

Let R represent the red marble, G the green marble, and B the blue marble.
The sample space consists of all possible results of this experiment.
Consider first drawing the red marble. The second draw can be either the red, green or blue
marble and so on. The sample space will have size 3 · 3 since there are three possibilities for
the first draw and three possibilities for the second draw. The sample space is
S = {(R, R),(R, G),(R, B),(G, R),(G, G),(G, B),(B, R),(B, G),(B, B)}
If after the first draw we do not replace the first marble, then the sample space has size 3 · 2
since there are three possibilities for the first draw and only two for the second draw. Then
the sample space is
S = {(R, G),(R, B),(G, R),(G, B),(B, R),(B, G)}

b) P = First green and second blue

Prob of getting first green is 1/5 and second blue, if repetition is allowed is 1/5

Thus prob is 1/5*1/5=1/25

c) P = First green and second blue ( without repetition )

1/5 * 1/4 = 1/20

This is because second time the green marbel is not replaced and hence total marble reduced from 5 to 4.

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