Question

n a political science class there are 8 men and 13 women. 2 students are randomly selected to present a topic. What is the probability that at least 1 of the 2 students selected is female? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

total number of students = 8 + 13 = 21

Probability that at least 1 of the 2 students selected is female = 1- Probability of 0 female student in 2 selected students

using combination, probability of 0 female student in 2 student = (number of ways of selecting 2 male)/(total number of ways of selecting 2 students out of total)

where number of ways of selecting 2 male = Combination(8,2) = 8!/((8-2)!*2!) = 28

and total number of ways of selecting 2 students out of total = Combination(21,2) = 21!/((21-2)!*2!) = 210

this implies

Probability of 0 female student in 2 selected students = 28/210 = 0.1333

and

Probability that at least 1 of the 2 students selected is female = 1- Probability of 0 female student in 2 selected students

= 1 - 0.1333

= 0.8667 (rounded to 4 decimals)