line Math 120 Intro Prob and Stats
Question 18, 5.5.61
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The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of five students and nine faculty. (a) What is the probability of selecting a jur of all students? (b) What is the probability of selecting a jury of all faculty? © What is the probability of selecting a jury of two students and two faculty?
(a) What is the probability of selecting a jury of all students?
0.00500 (Round to five decimal places as needed.)
(b) What is the probability of selecting a jury of all faculty?
(Round to five decimal places as needed.)

Ask by Washington Wright. in the United States

Mar 25,2025

Question

line Math 120 Intro Prob and Stats
Question 18, 5.5.61
HW Score: , 18 of 36 points
Save
ework
Part 2 of 3
Points: 0 of 1

The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of five students and nine faculty. (a) What is the probability of selecting a jur of all students? (b) What is the probability of selecting a jury of all faculty? © What is the probability of selecting a jury of two students and two faculty?
(a) What is the probability of selecting a jury of all students?
0.00500 (Round to five decimal places as needed.)
(b) What is the probability of selecting a jury of all faculty?
(Round to five decimal places as needed.)

Ask by Washington Wright. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

Let

$$
T = \binom{14}{4}
$$

be the total number of ways to choose 4 individuals from 14 (5 students + 9 faculty) and

$$
F = \binom{9}{4}
$$

be the number of ways to choose 4 faculty members from the 9. Then the probability of selecting a jury of all faculty is

$$
P(\text{all faculty}) = \frac{\binom{9}{4}}{\binom{14}{4}}.
$$

We compute:

$$
\binom{9}{4} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = 126,
$$

and

$$
\binom{14}{4} = \frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1} = 1001.
$$

Thus,

$$
P(\text{all faculty}) = \frac{126}{1001} \approx 0.12587.
$$

So, the probability of selecting a jury of all faculty, rounded to five decimal places, is

$$
\boxed{0.12587}.
$$
The probability of selecting a jury of all faculty is approximately 0.12587.