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
