Question

suppose that a certain college class contains 51 students. of these, 23 are sophomores, 30 are mathematics 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 sophomore and a mathematics major?
(b) given that the student selected is a sophomore, what is the probability that she is also a mathematics major?

write your responses as fractions. (if necessary, consult a list of formulas.)

Explanation:

Define the given sets

Using the Probability of Events knowledge point

$$
LATEXBLOCK0
$$

Find the union of the sets

Using the Addition Rule of Probability knowledge point

$$
LATEXBLOCK1
$$

Calculate the intersection of the sets

Using the Addition Rule of Probability knowledge point

$$
LATEXBLOCK2
$$

Solve part (a)

Using the Probability of Events knowledge point

$$
LATEXBLOCK3
$$

Solve part (b)

Using the Conditional Probability knowledge point

$$
LATEXBLOCK4
$$

Answer:

(a) \(\frac{8}{51}\)

(b) \(\frac{8}{23}\)