Suppose I look at all the students in my class who are either freshmen, sophomor

Question

Suppose I look at all the students in my class who are either freshmen, sophomores, juniors, or seniors, and I put all of their names into a hat. I plan to draw out two names. Which of the following are sample spaces? If any of them aren't sample spaces, explain (in one sentence or so) why not. a) S_1 = {FF, FS, FJ, FR, SE, SS, SJ, SR, JE, JS, JJ, JR, RF, RS, RI, RR} where F represents drawing a freshman's name, S represents drawing a sophomore's name, J represents drawing a junior's name, and R represents drawing a senior's name, and the draws are in order. b) S_2 = {both students are sophomores, at least one student is not a sophomore} c) S_3 = {only the first student is a sophomore, only the second student is a sophomore, neither student is a sophomore} d) S4 = {the first student is a sophomore, the second student is a sophomore, neither student is a sophomore} As before, I've put the names of all the undergraduate students in this class into a hat, and an experiment consists of drawing two students names out. I want to measure how many sophomore students I draw from the hat. Write down a good sample space that measures what I want.

Explanation / Answer

4. Option(a) is the correct sample space, as each of the students selected will have 4 possibilities. So total number of outcomes = 4 * 4 = 16.

Option (b) is not a correct choice, as both the students need not be sophomore. It is a subset of the sample space.

Option (c) is not a correct choice, as both the students can be sophomore also. It is a subset of the sample space.

Option (d) is not a correct choice in similar way.

5. Here the sample space will be same as earlier one in Option 4(a) as possible outcomes and number of experiments are same. We can consider a subset of the sample space for our convenience as {SS, SF, SJ, SR, FS, JS, RS}.

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