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 □ outcomes in the sample space.
(type a whole number.)

Explanation:

Step1: Analyze the sample space elements

The first event has 4 grades (F, So, J, Se) and the second event has 2 employment - statuses (E, U). Each grade is combined with each employment - status.
For grade F: combinations are FE, FU
For grade So: combinations are SoE, SoU
For grade J: combinations are JE, JU
For grade Se: combinations are SeE, SeU

Step2: Count the number of outcomes

Using the counting principle \(n = n_1\times n_2\), where \(n_1 = 4\) (number of grades) and \(n_2=2\) (number of employment - statuses). So \(n=4\times2 = 8\)

Answer:

The sample space is \(\{FE, FU, SoE, SoU, JE, JU, SeE, SeU\}\) (Option D). There are \(8\) outcomes in the sample space.