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 (se)) and then their employment status (employed (e), unemployed (u))
identify the sample space.
a. {fe, fu, soe, sou, je, ju, see, seu, ue, uu}
b. {fe, fu, fj, soe, sou, soj, je, ju, jj}
c. {fe, fu, fj, soe, sou, soj, je, ju, jj, see, seu, sej}
d. {fe, fu, soe, sou, je, ju, see, seu}
there are 8 outcomes in the sample space.
(type a whole number.)
choose the correct tree diagram below.
a.
b.
c.
d.

Explanation:

Step1: Determine the sample space

The first event is the grade (4 options: F, So, J, Se) and the second event is the employment status (2 options: E, U). Each grade - employment status combination is an outcome.
For grade F: outcomes are FE, FU
For grade So: outcomes are SoE, SoU
For grade J: outcomes are JE, JU
For grade Se: outcomes are SeE, SeU

Step2: Count the number of outcomes

Using the multiplication principle \(n = 4\times2=8\)

Answer:

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