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 library tutoring center soup kitchen hospital
number of students 14 15 8 13
three students from the club are selected at random, one at a time without replacement. what is the probability that none of the three students volunteer at the soup kitchen? do not round your intermediate computations. round your final answer to three decimal places.

Explanation:

Step1: Calculate total number of students

The total number of students is the sum of students in each location. So, $13 + 8+15 + 14=50$.

Step2: Calculate probability of not - selecting from soup kitchen in first draw

The number of students not in the soup kitchen is $50 - 8=42$. The probability of not selecting a student from the soup kitchen in the first draw is $\frac{42}{50}$.

Step3: Calculate probability of not - selecting from soup kitchen in second draw

Since we are drawing without replacement, for the second draw, there are $49$ students left and $41$ students who are not from the soup kitchen. So the probability is $\frac{41}{49}$.

Step4: Calculate probability of not - selecting from soup kitchen in third draw

For the third draw, there are $48$ students left and $40$ students who are not from the soup kitchen. So the probability is $\frac{40}{48}$.

Step5: Calculate probability of not - selecting from soup kitchen in fourth draw

For the fourth draw, there are $47$ students left and $39$ students who are not from the soup kitchen. So the probability is $\frac{39}{47}$.

Step6: Calculate the overall probability

The probability that none of the four students are from the soup kitchen is the product of the probabilities of each draw. So $P=\frac{42}{50}\times\frac{41}{49}\times\frac{40}{48}\times\frac{39}{47}\approx0.399$.

Answer:

$0.399$