Question
In: Statistics and Probability
A math class consists of 29 students, 17 female and 12 male. Three students are selected...
A math class consists of 29 students, 17 female and 12 male.
Three students are selected at random, one at a time, to
participate in a probability experiment (selected in order without
replacement).
(a) What is the probability that a male is selected, then two
females?
(b) What is the probability that a female is selected, then two
males?
(c) What is the probability that two females are selected, then one
male?
(d) What is the probability that three males are selected?
(e) What is the probability that three females are selected?
Solutions
Expert Solution
A math class consists of 29 students, 17 female and 12 male.
Three students are selected at random, one at a time, to
participate in a probability experiment (selected in order without
replacement).
(a) probability that a male is selected, then two females
Probability of selecting a male first = Number of males / Total number of students = 12/29
Once, male is selected , Number of male left = 11, Total number of students = 28
Probability of selecting a female as second = Number of females / Total number of students = 17/28
Once, male and female are selected , Number of females left = 16, Total number of students = 27
Probability of selecting a female as third = Number of females / Total number of students = 16/27
probability that a male is selected, then two females=
(12/29)x(17/28)x(16/27) = 3264/21924=0.148877942
probability that a male is selected, then two
females=3264/21924=0.148877942
(b) What is the probability that a female is selected, then two
males?
Probability of selecting a female first = Number of females / Total number of students = 17/29
Once, female is selected , Number of female left = 16, Total number of students = 28
Probability of selecting a male as second = Number of males / Total number of students = 12/28
Once, male and female are selected , Number of males left = 11, Total number of students = 27
Probability of selecting a male as third = Number of males / Total number of students = 11/27
probability that a female is selected, then two males= (17/29)x(12/28)x(11/27)=2244/21924=0.102353585
probability that a female is selected, then two males=2244/21924=0.102353585
(c) What is the probability that two females are selected, then one
male?
Probability of selecting a female first = Number of females / Total number of students = 17/29
Once, female is selected , Number of female left = 16, Total number of students = 28
Probability of selecting a female as second = Number of females / Total number of students = 16/28
Once, two females are selected , Number of females left = 15, Total number of students = 27
Probability of selecting a male as third = Number of males / Total number of students = 12/27
probability that two females are selected, then one male = (17/29)x(16/28)x(12/27) = 3264/21924 = 0.148877942
probability that two females are selected, then one
male = 3264/21924 = 0.148877942
(d) What is the probability that three males are selected?
Probability of selecting a male first = Number of males / Total
number of students = 12/29
Once, male is selected , Number of male left = 11, Total number of students = 28
Probability of selecting a male as second = Number of males / Total number of students = 11/28
Once, two males are selected , Number of males left = 10, Total number of students = 27
Probability of selecting a male as third = Number of males / Total number of students = 10/27
probability that three males are selected = (12/29)x(11/28)x(10/27) =1320/2194=0.060207991
probability that three males are selected =1320/2194=0.060207991
(e) What is the probability that three females are selected?
Probability of selecting a female first = Number of females / Total number of students = 17/29
Once, female is selected , Number of female left = 16, Total number of students = 28
Probability of selecting a female as second = Number of females / Total number of students = 16/28
Once, two females are selected , Number of females left = 15, Total number of students = 27
Probability of selecting a female as third = Number of females / Total number of students = 15/27
probability that three females are selected = (17/29)x(16/28)x(15/27) = 4080/21924=0.186097427
probability that three females are selected = 4080/21924 = 0.186097427
orchestra answered 2 years agoRelated Solutions
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