Question

A bandleader randomly select's two students out of 100 bandmembers if you and your brother are both bandmembers what is the probability that you are both selected?

Answer 1

There are 100 * 99 = 9900 different ways to choose two students out of 100 bandmembers. You and our brother are 2 of that ways: you being selected first and you being selected second. Therefore the probability that you two are selected is 2 / 9900 = 0,000202. You can also think as the probability of you being selected among 100 bandmembers, which is 1/100, times the probability of your brother being selected among 99 members, which is 1/99 => (1/100) * (1/99) = 1/ (100*99) = 1 / 9900; plus the same for your brother being selected first and you second => [1/9900] * 2 = 2/9900, which is the same calculated above.