Question

suppose there are 10 female students and 30 male students in a classroom. the students are leaving the classroom at random one by one.

what is the probability P(L) that the first five students leave the class in the following order: female, male, female, female and male.

so P(L) is?

Answer 1

First: Female:

Male students = 30

Female students = 10

Total students =40

P(First: Female:) = 10/40 = 0.25

Second: Male:

Male students = 30

Female students = 9

Total students =39

P(Second: Male:) = 30/39 = 0.7692

Third: Female:

Male students = 29

Female students = 9

Total students =38

P(:Third: Female) = 9/18 = 0.2368

Fourth: Female:

Male students = 29

Female students = 8

Total students =37

P(:Fourth: Female) = 8/37= 0.2162

Fifth Male:

Male students = 29

Female students = 7

Total students =36

P(Fifth Male) = 29/36 = 0.8056

So,

the probability P(L) that the first five students leave the class in the following order: female, male, female, female and male = 0.25 X 0.7692 X 0.2368 X 0.2162 X 0.8056 = 0.007931

So,

Answer is:

0.007931