Question

A class consists of 60 boys and 40 girls. If two students are chosen at random, what is the probability that i) both are boys ii) both are girls iii) one boy and one girl? ​

Answer 1

b: boys, g: girls
Without replacement

i) P(b and b) = 60/100 * 59/ 99 = 59/165 = 0.358
ii) P(g and g) = 40/100 * 39/99 = 0.158
iii) we can solve this question using hyper geometric distribution:
(60C1 * 40C1)/ 100C2 = 0.48