Show all of your work for each problem. A group of college students is summarize
ID: 3300783 • Letter: S
Question
Show all of your work for each problem. A group of college students is summarized in this table by class and major. (a) If one student is selected, what is the probability of selecting either an English major or a junior? (b) If one student is selected, what is P (senior | math major)? c) If 3 students are selected randomly, what is the probability of selecting one student from each major? (d) If 3 students are selected randomly, what is the probability of selecting exactly 1 math major? (e) If 3 students are selected randomly, what is the probability of at least 1 physics major?Explanation / Answer
Total number of students = 1 + 2 + 2 + 3 + 1 + 1 = 10
(a) Number of students who are English majors or juniors
= 1 + 2 + 2 + 1 = 6
Probability that the selected student is an English major or a junior
= 6/10 = 0.6
(b) Number of students who are seniors given they are math majors
= 3
=> P ( senior | math major ) = 3/10 = 0.3
(c) Number of math majors = 4
Number of physics majors = 3
Number of English majors = 3
Probability of selecting (math,physics,english) majors = 4/10 * 3/9 * 3/8 = 0.05
Probability of selecting (math,english,physics) majors = 4/10 * 3/9 * 3/8 = 0.05
Probability of selecting (physics,math,english) majors = 3/10 * 4/9 * 3/8 = 0.05
Probability of selecting (physics,english,math) majors = 3/10 * 3/9 * 4/8 = 0.05
Probability of selecting (english,math,physics) majors = 3/10 * 4/9 * 3/8 = 0.05
Probability of selecting (english,physics,math) majors = 3/10 * 3/9 * 4/8 = 0.05
=> Probability of selecting one student from each major = 6 * 0.05 = 0.3
(d) The probability that the first student is not a math major = 6/10.
The probability that the second is also not a math major = 5/9.
The probability that the third is also not a math major = 4/8.
=> Probability that all three are not math majors = 6/10 * 5/9 * 4/8 = 0.17
=> Probability that atleast one is a math major = 1 - 0.17 = 0.83
(e) Probability that there are no physics majors = 7/10 * 6/9 * 5/8 = 0.2917
=> Probability that there is atleast one physics major = 1 - 0.2917 = 0.7083