Question

a club with 50 college students is doing volunteer work this semester. each student is volunteering at one of four locations. here is a summary.

location	number of students
nursing home	8
pet shelter	13
hospital	18

three students from the club are selected at random, one at a time without replacement. what is the probability that the first student volunteers at the hospital and the other two do not?

do not round your intermediate computations. round your final answer to three decimal places.

Explanation:

Step1: Find probability first student is at hospital

Total students = 50, hospital students = 18. So probability first is hospital: $\frac{18}{50}$.

Step2: Find probability second student not at hospital

After first (hospital) is chosen, remaining students = 49, non - hospital students = 50 - 18 = 32. Probability second not hospital: $\frac{32}{49}$.

Step3: Find probability third student not at hospital

After two are chosen, remaining students = 48, non - hospital students = 31. Probability third not hospital: $\frac{31}{48}$.

Step4: Multiply the probabilities

Probability = $\frac{18}{50}×\frac{32}{49}×\frac{31}{48}$
First, calculate $\frac{18}{50}×\frac{32}{49}=\frac{18×32}{50×49}=\frac{576}{2450}$
Then, $\frac{576}{2450}×\frac{31}{48}=\frac{576×31}{2450×48}=\frac{17856}{117600}$
Simplify $\frac{17856}{117600}= 0.1518367347$ (after division)
Round to three decimal places: 0.152

Answer:

0.152