Question

suppose that a certain college class contains 58 students. of these, 30 are seniors, 35 are history 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 senior and a history major?
(b) given that the student selected is a senior, what is the probability that he is also a history major?

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

Explanation:

Define the given sets and total outcomes

Using the Probability of Events knowledge point

$$
LATEXBLOCK0
$$

Calculate the intersection of the two sets

Using the Probability of Events knowledge point

$$
LATEXBLOCK1
$$

Calculate the probability for part (a)

Using the Probability of Events knowledge point

$$ P(A \cap B) = \frac{N(A \cap B)}{N(S)} = \frac{13}{58} $$

Calculate the conditional probability for part (b)

Using the Conditional Probability knowledge point

$$ P(B \mid A) = \frac{N(A \cap B)}{N(A)} = \frac{13}{30} $$

Answer:

Question 1

(a) What is the probability that the student is both a senior and a history major? <blank>\(\frac{13}{58}\)</blank>

Question 2

(b) Given that the student selected is a senior, what is the probability that he is also a history major? <blank>\(\frac{13}{30}\)</blank>