Question

In a class of 30 students there are 17 girls. two students are picked randomly to represent the class in the SRC. determine the probability that:

a. both students are boys
b. both students are girls
c. one of the students is a boy

Answer 1

See below in bold,.

Explanation:

There are 30-17 = 13 boys in the class.

a. Prob(First is a boy ) = 13/30 and Prob( second is a boy = 12/29).

As these 2 events are independent:

Prob( 2 boys being picked) = 13/30 * 12/29 = 26/145 or 0.179 to the nearest thousandth.

b. By a similar method to a:

Prob ( 2 girls being picked) = 17/30 * 16/29 = 136/435 = 0.313 to the nearest thousandth.

c. Prob (First student is a boy and second is a girl) = 13/30 * 17/29 = 221/870.

Prob ( first student is a girl and second is a boy) = 17/30 * 13/29 = 221/870

These 2 events are not independent so they are added:

Prob( one of the students is a boy) = 2 (221/870 = 221/435 = 0.508 to the nearest thousandth.