Question

a university class has 30 students: 17 are business majors, 5 are art majors, and 8 are nursing 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 business majors will be selected? do not round your intermediate computations. round your final answer to three decimal places.

Explanation:

Step1: Probability first is business

There are 17 business majors out of 30 students. So the probability the first student is a business major is $\frac{17}{30}$.

Step2: Probability second is business

After selecting one business major, there are 16 business majors left and 29 students left. So the probability the second student is a business major is $\frac{16}{29}$.

Step3: Multiply the probabilities

To find the probability of both events happening (first and second are business majors), we multiply the two probabilities: $\frac{17}{30} \times \frac{16}{29}$.
Calculating this: $\frac{17\times16}{30\times29}=\frac{272}{870}\approx0.3126437$. Rounding to three decimal places gives 0.313.

Answer:

0.313