$$ (5.5,5.6,5.7) $$ 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 jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) 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? $$ 18,5.5 .61 $$ $$ \square $$ (Round to five decimal places as needed.)

Question

UpStudy AI · Accepted Answer

Given that there are 5 students and 9 faculty, the total number of individuals is $$ 5+9=14 $$.

**Step 1. Find the total number of ways to select 4 individuals from 14.**

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

**Step 2. Find the number of ways to select an all-student jury.**

Since we need to choose 4 students out of 5:

$$
\text{Student ways} = \binom{5}{4} = 5.
$$

**Step 3. Compute the probability.**

$$
\text{Probability} = \frac{\text{Student ways}}{\text{Total ways}} = \frac{5}{1001}.
$$

Rounded to five decimal places:

$$
\frac{5}{1001} \approx 0.00499.
$$
The probability of selecting a jury of all students is approximately 0.00499. **Step 1:** Total ways to select 4 individuals from 14 is 1001. **Step 2:** Ways to select 4 students from 5 is 5. **Step 3:** Probability = 5/1001 ≈ 0.00499

Upstudy AI Solution

Answer

Solution

The Deep Dive

(a) Probability of selecting a jury of all students

(b) Probability of selecting a jury of all faculty

© Probability of selecting a jury of two students and two faculty

Summary of Results

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