A box of 12 batteries has 3 defective ones. (Enter your probabilities as fractions.) (a) If 2 batteries are drawn from the box together, what is the probability that both are defective? (b) If 2 batteries are drawn from the box together, what is the probability that neither one is defective? (c) If 2 batteries are drawn from the box together, what is the probability that one is defective?

Suppose your hole cards are 7♥ 9♥, and your opponent’s hole cards are Q♣ 8♣. The flop and the turn are 3♥ 8♥ J♦ 2♣.  What is the probability that you get a flush on the river?

Suppose a fair die is rolled 18 times. (a) What is the probability p that a 2 will occur any given time the die is rolled? (Enter your probability as a fraction.) p = (b) What is the probability q that a 2 will not occur any given time the die is rolled? (Enter your probability as a fraction.) q = (c) What is n for this experiment? n = (d) What is the probability that a 2 will occur 7 times in the 18 rolls? (Round your answer to three decimal places.)

A bag contains 6 red balls and 7 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is white, given that the first ball is red? (b) What is the probability that the second ball is red, given that the first ball is white? (c) Answer part (a) if the first ball is replaced before the second is drawn.