Question

1. A fair six-sided die has two sides painted red, 3 sides painted blue and one side painted yellow.

The die is rolled and the color of the top side is recorded.

1. List all possible outcomes of this random experiment
2. Are the outcomes equally likely? Explain
3. Make a probability distribution table for the random variable X: color of the top side

      

2. If a pair of dice painted the same way as in problem 1 is rolled, find the probability of the event

                    a.   “both dice roll red”

                    b.    “neither die rolls red”

                    c.     “exactly one die rolls red”

Answer 1

1) a) possible outcomes = {red, blue, yellow}

b) No, the outcomes are not equally likely. Because number of elements of the outcomes are different for each element.

c)

Color               Probability

red                       2/6 = 1/3

blue                     3/6 = 1/2

yellow                  1/6

2) a) P(both dice roll red) = P(red) * P(red) = 1/3 * 1/3 = 1/9

b) P(neither die rolls red) = P(not red) * P(not red) = (1 - 1/3) * (1 - 1/3) = 4/9

c) P(exactly one die rolls red) = 2C1 * 1/3 * (1 - 1/3) = 4/9