Question

a university class has 27 students: 13 are history majors, 5 are nursing majors, and 9 are accounting majors. (each student has only one of these majors.) the professor is planning to select two of the students for a demonstration. the first student will be selected at random, and then the second student will be selected at random from the remaining students. what is the probability that two nursing majors will be selected? do not round your intermediate computations. round your final answer to three decimal places.

Explanation:

Step1: Calculate probability of first nursing - major selection

The probability of selecting a nursing - major student on the first draw is the number of nursing - major students divided by the total number of students. There are 5 nursing - major students and 27 total students. So the probability $P_1=\frac{5}{27}$.

Step2: Calculate probability of second nursing - major selection

After one nursing - major student is selected, there are 4 nursing - major students left and 26 total students left. So the probability of selecting a nursing - major student on the second draw given that a nursing - major student was selected on the first draw is $P_2 = \frac{4}{26}$.

Step3: Calculate the joint probability

The probability that both events occur (selecting two nursing - major students) is the product of the probabilities of each event. So $P = P_1\times P_2=\frac{5}{27}\times\frac{4}{26}=\frac{20}{702}\approx0.028$.

Answer:

0.028