Consider the following. (Assume that what is observed are the numbers that face up.) HINT Two indistinguishable dice are rolled; the numbers add to 6. Describe the sample space S of the experiment. (Select all that apply.) (4,4) (4,5) (4,6) (6,6) (6,7) (2,2) (2,3) (2,4) (2,5) (2,6) (4,4) (4,5) (4,6) (4,7) (6,6) (5,5) (5,6) (5,7) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) ☐ (5,5) (5,6)

Suppose that we roll two fair dice, one red and one blue. Then there are 36 possible outcomes in the sample space, as shown in the table below. Blue Die 1 4 6. 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 84 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) A 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4)| (6,5) (6,6) Suppose we write the sample space in terms of the number of dots facing up on the two dice. That is, write S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Use the table to answer each of the following: Complete the probability distribution function (pdf). Enter your answer as a fraction. Sample space Probability 2 3 4.

The following test scores are for two classes that took the same test. (The highest possible score on the test was 60.) Class 1 (24 scores): 37, 45, 52, 55, 11, 55, 44, 55, 35, 25, 52, 42, 35, 21, 42, 52, 41, 40, 34, 51, 41, 41, 41, 41 Class 2 (25 scores): 50, 40, 40, 23, 40, 50, 31, 31, 40, 31, 31, 31, 53, 33, 33, 35, 55, 24, 39, 40, 41, 59, 41, 39, 46 Form a back-to-back stem and leaf plot with one stem. Put the leaves for one class on the right side of the stem and the leaves for the other class on the left side. Record the leaves in increasing order from the stem. Leaf (Class 1) Stem Leaf (Class 2) 4 3 1

2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer: