Question

a student entering a doctoral program in educational psychology is required to select three courses from the list of courses provided as part of his or her program.
(a) list all possible three - course selections.
(b) comment on the likelihood that epr 695, epr 638, and epr 654 will be selected.
click the icon to view the course list.
(a) select all the possible three - course selections below.
a. 695, 654, 622
b. 624, 654, 622
c. 695, 624, 654
d. 638, 624, 654
e. 695, 638, 624
f. 695, 624, 622
g. 622, 676, 622
h. 695, 638, 622
i. 624, 622, 624
j. 638, 654, 622
k. 695, 695, 638
l. 638, 624, 622
m. 695, 695
n. 695, 638, 654
(b) there is a \square in \square chance that these courses will be selected.
(simplify your answer.)

Explanation:

Step1: Identify valid 3-course sets

Valid sets have 3 unique courses (no repeats, correct count):
A. 695, 654, 622; B. 624, 654, 622; C. 695, 624, 654; D. 638, 624, 654; E. 695, 638, 624; F. 695, 624, 622; H. 695, 638, 622; J. 638, 654, 622; L. 638, 624, 622; N. 695, 638, 654
Invalid sets (repeats/incorrect count): G, I, K, M
Count of valid total selections: $10$

Step2: Count target selection

The target set (EPR 695, 638, 654) is option N, so there is $1$ favorable outcome.

Step3: Calculate probability

Probability = $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$ = $\frac{1}{10}$

Answer:

(a) The valid three-course selections are:
A. 695, 654, 622
B. 624, 654, 622
C. 695, 624, 654
D. 638, 624, 654
E. 695, 638, 624
F. 695, 624, 622
H. 695, 638, 622
J. 638, 654, 622
L. 638, 624, 622
N. 695, 638, 654

(b) There is a $\boldsymbol{1}$ in $\boldsymbol{10}$ chance that these courses will be selected.