Question

identify the sample space of the probability experiment and determine the number of outcomes in the sample space. draw a tree diagram.
determining a persons grade (freshman (f), sophomore (so), junior (j), senior (sc)) and then their employment status (employed (e), unemployed (u))
identify the sample space.
o a. {fe, fu, soe, sou, je, ju, see, seu, ue, uu}
o b. {fe, fu, fj, soe, sou, soj, je, ju, jj}
o c. {fe, fu, fj, soe, sou, soj, je, ju, jj, see, seu, sej}
o d. {fe, fu, soe, sou, je, ju, see, seu}

Explanation:

Step1: Analyze the grade and employment status

There are 4 grades (freshman \(F\), sophomore \(So\), junior \(J\), senior \(Se\)) and 2 employment - statuses (employed \(E\), unemployed \(U\)).
For each grade, there are 2 possible employment - status outcomes.

Step2: List the sample - space elements

For freshman (\(F\)): the outcomes are \(FE\) (freshman - employed) and \(FU\) (freshman - unemployed).
For sophomore (\(So\)): the outcomes are \(SoE\) (sophomore - employed) and \(SoU\) (sophomore - unemployed).
For junior (\(J\)): the outcomes are \(JE\) (junior - employed) and \(JU\) (junior - unemployed).
For senior (\(Se\)): the outcomes are \(SeE\) (senior - employed) and \(SeU\) (senior - unemployed).

Answer:

D. \(\{FE,FU,SoE,SoU,JE,JU,SeE,SeU\}\)