Question

calculating theoretical probability
six students, michelle, nadir, olivia, parvi, quinn, and richard, are running for four identical positions on student council. what is the theoretical probability that nadir will be chosen as part of the group? enter your answer in fraction form.

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 favorable combinations

If Nadir is already chosen, we need to choose 3 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 favorable combinations divided by the total number of combinations. So $P=\frac{C(5,3)}{C(6,4)}=\frac{10}{15}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$