Homework #2-Chapter10&3 (20pts for turned in on time) 9. (13pts) A die has 6 fac

Question

Homework #2-Chapter10&3 (20pts for turned in on time) 9. (13pts) A die has 6 faces. 2 faces are colored blue, and 4 faces are colored red. (1) (2pts)if you roll the die once, and record the up-face color. What is the sample space? 2) (2pts)if you roll the die once, what is the probabilitythat the up-face color is Blue? (3) (7ps)lf you roll the die three times, and record the up-face value for each roll. One of the possible outcomes is (Red, Red, Red). By assuming the three rolls are independent, we can use the multiplication rule (see class PPT) to calculate the probability P(Red, Red, Red) Pl1 is red) P(d is red)'P(3rd is red) (2/3)2/3)(2/3)-8/27 Possible Outcome Probability (Red, Red, Red) (4) (2pts)What is the total probability of all possible outcomes? (Add probabilities of each outcome, including the one provided P (Red, Red, Red]).

Explanation / Answer

1) S = {red, blue}

2)P(Blue) = 2/6 = 1/3

4) 8/27 + 4/27 + 4/27 + 2/27 + 4/27 + 2/27 + 2/27 + 1/27 = 27/27 = 1

Outcom Probability (Red, Red, Red) 8/27 (Red, Red, Blue) 4/27 (Red, Blue, Red) 4/27 (Red, Blue, Blue) 2/27 (Blue, Red, Red) 4/27 (Blue, Blue, Red) 2/27 (Blue, Red, Blue) 2/27 (Blue, Blue, Blue) 1/27

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