For this problem, assume that three students are chosen from 3 freshmen, 7 sophomores, and 5 juniors. What is the probability of selecting 2 freshmen and 1 junior given that at least one freshman will be selected?

generals336 2021-01-17 Answered
For this problem, assume that three students are chosen from 3 freshmen, 7 sophomores, and 5 juniors.
What is the probability of selecting 2 freshmen and 1 junior given that at least one freshman will be selected?
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Expert Answer

falhiblesw
Answered 2021-01-18 Author has 97 answers
Step 1
Given: Number of Freshmen, Sophomores & juniors are 3, 7 & 5 respectively.
To find: Probability of selecting 2 freshmen, 1 junior given that at least one freshman will be selected.
Total number of students is equal to the sum of number of freshmen, sophomores and juniorsTotal number of students 3+7+5
=15 The formula which gives us the total number of ways of forming group of r objects, out of n objects is:
C(n,r)=n!r!(nr)
Step 2
Three students are selected from 3 freshmen, 7 sophomores and 5 juniors, Such that the at least 1 freshman is selected
The selection of one freshman can be done in P(3, 1) ways
P(3,1)=3!(31)!=3
Selection of one freshman can be done in 3 ways
The selection of remaining two students from 2 freshmen, 7 sophomores and 5 juniors.
Number of ways of selection two students out of (2+7+5)=14 students
C(14,2)=14!2!(142)!
C(14,2)=7×13
C(14,2)=91
Thus total number of possible ways of selection three students are =3×91=273
Step 3
Selection of two freshman from three freshmen is done in C(3, 2) ways
C(3,2)=3!2!(32)!
C(3, 2)=3
Thus, the selection of two freshman and one junior can be done in C(3, 2)×3 ways
C(3, 2)×3=3×3
C(3, 2)×3=9
The selection of two freshman and one junior can be done in 9 ways.
Step 4
Probability of selection of two freshman and one junior out of the total number of possible ways of selection three students such that at least one freshman is selected.
Number of favorable outcomes =9
Total number of outcomes =273
Probability =Number of favorable outcomestotal number of outcomes
Probability =9273
Probability =0.032
Answer:
Probability of selection of two freshman and one junior given that at least one freshman is selected is 0.032.
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