Question

Here is the information for a class on campus. We need to randomly select two students to interview. (We don't want to interview the same student twice.) Class Frequency Freshman 21 Sophomore 14 Junior 9 Senior 6

(a) Are the two student selections going to be independent?

(b) What is the probability that we choose a Freshman and then a Senior?

(c) What is the probability that we choose a Sophomore and then another Sophomore?

(d) What is the probability that we choose a Freshman and a Senior in any order?

(e) What is the probability that both students are at the same class level?

(f) What is the probability that both students are not at the same class level?

(g) We decide we need to interview more students. We decide to interview a total of 6 randomly chosen students. What is the probability that all the students chosen are freshmen?

Answer 1

Answer (a) The 2 student selections are not going to be independent as selection of first student impacts the probability of selection of second student.

Answer (b) Probability that we choose a Freshman and then a Senior = (No. of ways of selecting Freshman * No. of ways of selecting senior)/Total Number of ways of selecting 2 students

Probability that we choose a Freshman and then a Senior = (₂₁C₁*₆C₁)/(₅₀C₂*2) (We have multiplied 2 as for each selection there are two ways in which students can give interview)

Probability that we choose a Freshman and then a Senior = (21*6)/(1225*2) = 0.0514

Answer (c) Probability that we choose a Sophomore and then another Sophomore = (No. of ways of selecting 2 Sophomore)/Total Number of ways of selecting 2 students

Probability that we choose a Sophomore and then another Sophomore = (₂₁C₂*2)/(₅₀C₂*2) (We have multiplied 2 as for each selection there are two ways in which students can give interview)

Probability that we choose a Sophomore and then another Sophomore = (21*20)/(1225) = 0.3429

Answer (d) Probability that we choose a Freshman and a Senior in any order = (No. of ways of selecting Freshman * No. of ways of selecting senior)/Total Number of ways of selecting 2 students

Probability that we choose a Freshman and a Senior in any order = (₂₁C₁*₆C₁*2)/(₅₀C₂*2)

Probability that we choose a Freshman and a Senior in any order = (21*6*2)/(1225*2) = 0.1029

Answer (e) Probability that both students are at the same class level = (No. of ways of selecting students from same level)/Total Number of ways of selecting 2 students

Probability that both students are at the same class level = ((₂₁C₂+₁₄C₂+₉C₂+₆C₂)*2)/(₅₀C₂*2)

Probability that both students are at the same class level = ((210+91+36+15)*2)/(1225*2)

Probability that both students are at the same class level = 352/1225 = 0.2873

We have answered 5 parts