Question

Suppose that a certain college class contains 43 students. Of these, 25 are freshmen, 25 are business majors, and 6 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a freshman and a business major? (b) Given that the student selected is a business major, what is the probability that she is also a freshman? Write your responses as fractions. (If necessary, consult a list of formulas.)

Answer 1

The probability that a student is both a freshman and a business major is 625/1849. Given that the student selected is a business major, the probability that she is also a freshman is 125/185.

Step-by-step explanation:

(a) To find the probability that a student is both a freshman and a business major, we need to find the overlap between the two groups. The probability of being a freshman is 25 out of 43 students, and the probability of being a business major is 25 out of 43 students. Since there are 43 students in total, the probability that a student is both a freshman and a business major is the product of the two probabilities:

P(Freshman AND Business Major) = P(Freshman) * P(Business Major) = 25/43 * 25/43 = 625/1849

(b) Given that the student selected is a business major, we can use conditional probability to find the probability that she is also a freshman. The probability of being a freshman AND a business major is 625/1849 (from part a), and the probability of being a business major is 25/43. Therefore, the conditional probability of being a freshman given that she is a business major is:

P(Freshman | Business Major) = P(Freshman AND Business Major) / P(Business Major) = (625/1849) / (25/43) = 625/925 = 125/185