Math word problem

Question

There are nine cards from a deck in a pile on the table. Five of the cards are red cards, and four of the cards are black cards. The cards are face down and three of them are selected at random. a.) What is the probability that all three of the cards selected are red? b). What is the probability that all three of the cards selected are black? c). What is the probability that at least one of the cards selected is red?

Answer 1

a) Prob(1st card red) * Prob(2nd card red | 1st card red) * Prob(3rd card red | 1st & 2nd cards red)

= 5/9 * 4/8 * 3/7

b) 4/9 * 3/8 * 2/7

c) 1 minus the probability given in b)