Question

Each card in a stack of 20 cards is numbered 1-20. If two cards are drawn at random and not replaced, what is the probability that both cards are odd and divisible by 3?

Answer 1

27/1444

Explanation:

there are 10 odd numbered cards and 3, 9, 15 are divisible by 3. also, 6, 12, 18 are divisible by 3.

P(1st card is odd and divisible by 3) = 10/20 X 6/20 = 60/400

now we have 19 cards remaining. we have 10 even numbered cards and 9 odd numbered cards. there are

P(2nd card is odd and divisible by 3) = 9/19 X 5/19 = 45/361

P(both cards are odd and divisible by 3) = 60/400 X 45/361 = 27/1444