Question

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?

   

Answer 1

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