1. A box contains 3 marbles, 1 red, 1 green and 1 blue. Consider an experiment t

Question

1. A box contains 3 marbles, 1 red, 1 green and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. (15 points - 3pts/question) a. List the elements in the sample space for this experiment. b. Which outcomes are in the event that at least 1 marble is red? c. Which outcomes are in the event that both marbles are the same color? d. List the elements in the sample space when the second marble is drawn without first replacing the first marble. e. What is the probability that at least 1 marble selected is red

Explanation / Answer

Let R denote red, G denote green and B denote blue

a) Sample space, S = {RR, RG, RB, GR, GG, GB, BR, BG, BB}

b) At least one marble is red = {RR, RG, RB, GR, BR}

c) Both marbles are same color = {RR, GG, BB}

d) Sample space, without replacement = {RG, RB, GR, GB, BR, BG}

e) P(at least one marble is red) = Number of cases with at least 1 red marble/Total number of outcomes

= 5/9

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