A student placement center has requests from five students for interviews regarding employment with a particular consulting firm. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students; these two will be randomly selected from among the five.

(a) What is the probability that both selected students are statistics majors?

(b) What is the probability that both students are math majors?

(c) What is the probability that at least one of the students selected is a statistics major?

(d) What is the probability that the selected students have different majors?

Answer: a) 1 / 10

b) 3 / 10

c) 1 / 5

d) 3 / 5

Step-by-step explanation:

Total number of requests five students for interviews regarding employment with the consulting firm = 5

Number of students that are maths majors = 3

Probability of selecting a maths student is 3 / 5

Number of students that are statistics majors = 2

Probability of selecting a statistics student is 2 / 5

a) the probability that both selected students are statistics majors

= 2 / 5 * 1 / 4 = 2 / 20 = 1 / 10

b) the probability that both students are math majors

= 3 / 5 * 2 / 4 = 6 / 20 = 3 / 10

c) the probability that at least one of the students selected is a statistics major will be p (one statistics and the other, maths) + p (one maths and the other, statistic) - p (both are mathematics)

= (2 / 5 * 1 / 4) + (2 / 5 * 3 / 4) - (3 / 5 * 2 / 4)

= 2 / 10 + 6 / 20 - 6 / 20

= 1 / 5 + 3 / 10 - 3 / 10

= 1 / 5

d) the probability that the selected students have different majors is p (one is maths and the other is statistics) + p (one is statistics and the other is maths)

(3 / 5 * 2 / 4) + (2 / 5 * 3 / 4)

= 6 / 20 + 6 / 20 = 12 / 20

= 3 / 5