calculating theoretical probability\nsix students, michelle, nadir, olivia, parvi, quinn, and richard, are…

Explanation:

Step1: Calculate total combinations

The number of ways to choose 4 students out of 6 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 6$ and $r=4$. So $C(6,4)=\frac{6!}{4!(6 - 4)!}=\frac{6!}{4!2!}=\frac{6\times5}{2\times1}=15$.

Step2: Calculate combinations with Nadir

If Nadir is already chosen, we need to choose 3 more students out of the remaining 5. Using the combination formula with $n = 5$ and $r = 3$, we have $C(5,3)=\frac{5!}{3!(5 - 3)!}=\frac{5!}{3!2!}=\frac{5\times4}{2\times1}=10$.

Step3: Calculate probability

The probability $P$ that Nadir is chosen is the number of combinations with Nadir divided by the total number of combinations. So $P=\frac{C(5,3)}{C(6,4)}=\frac{10}{15}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$