Question

if 4 students are chosen as representatives in the day 3 question, what is the probability of not being chosen as a representative?

Explanation:

1. Assume the total number of students is \(n\):

• The probability of being chosen as a representative when 4 students are chosen out of \(n\) is \(P(\text{chosen})=\frac{4}{n}\).
• The probability of not - being chosen is \(P(\text{not chosen}) = 1 - P(\text{chosen})\).

1. If we assume there are 16 students (\(n = 16\)):

• The probability of being chosen is \(\frac{4}{16}=\frac{1}{4}\).
• The probability of not - being chosen is \(1-\frac{1}{4}=\frac{3}{4}\).

Since the total number of students is not given in the problem, if we assume there are 16 students (a common - sense assumption for multiple - choice problems where the options seem to be in simple fraction form), the probability of not being chosen as a representative when 4 students are chosen out of 16 is \(\frac{3}{4}\).

Step 1: Define probability of being chosen

Let the total number of students be \(n\). The probability of being chosen as a representative when 4 students are chosen is \(\frac{4}{n}\).

Step 2: Calculate probability of not being chosen

The probability of not being chosen \(P = 1-\frac{4}{n}\). Assuming \(n = 16\), \(P=1 - \frac{4}{16}=\frac{16 - 4}{16}=\frac{12}{16}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)