# Here is the information for a

Here is the information for a class on campus. We need torandomly select two students to interview. (We don’t want tointerview the same student twice.) Class Frequency Freshman 21Sophomore 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 aSenior?

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

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

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

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

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

Answer:

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

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

Probability that we choose a Freshman and then a Senior =(_{21}C_{1}*_{6}C_{1})/(_{50}C_{2}*2)(We have multiplied 2 as for each selection there are two ways inwhich students can give interview)

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

Answer (c) Probability that we choose a Sophomore and thenanother Sophomore = (No. of ways of selecting 2 Sophomore)/TotalNumber of ways of selecting 2 students

Probability that we choose a Sophomore and then anotherSophomore =(_{21}C_{2}*2)/(_{50}C_{2}*2) (Wehave multiplied 2 as for each selection there are two ways in whichstudents can give interview)

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

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

Probability that we choose a Freshman and a Senior in any order=(_{21}C_{1}*_{6}C_{1}*2)/(_{50}C_{2}*2)

**Probability that wechoose 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 classlevel = (No. of ways of selecting students from same level)/TotalNumber of ways of selecting 2 students

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

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

**Probabilitythat both students are at the same class level = 352/1225 =0.2873**

We have answered 5 parts