Question

A college survey found that 6 out of 24 students walk to college. If 3 students are selected at random without replacement, what is the probability that all 3 walk to college?

• A. $\text{P(E)}=\frac{23}{506}$
• B. $\text{P(E)}=\frac{5}{506}$
• C. $\text{P(E)}=\frac{1}{506}$
• D. $\text{P(E)}=\frac{1}{605}$

Answer 1

The correct option is B $\text{P(E)}=\frac{5}{506}$

Given,
Total number of students surveyed $=24$
Number of student walk to college $=6$

Probability of choosing first student who walk to college is $\text{P(A)}=\frac{6}{24}=\frac{1}{4}$

Probability of choosing second student who walk to college is $\text{P(B)}=\frac{5}{23}$

Probability of choosing third student who walk to college is $\text{P(C)}=\frac{4}{22}=\frac{2}{11}$

Now, we have to find probablity of choosing 3 students at random that walk to college.
$\Rightarrow \text{P(A,B and C)}=\text{P(E)}=\text{P(A)}\times \text{P(B)}\times \text{P(C)}$

$\Rightarrow \text{P(E)}=\frac{1}{4}\times \frac{5}{23}\times \frac{2}{11}=\frac{5}{506}$