1. Clara and Naomi take a term test in discrete mathematics. The probability that Clara passes is 0.89 and the probability that Naomi passes is 0.70. Assuming that the events "Clara passes" and "Naomi passes” are independent, find the probability that Clara or Naomi, or both, pass the the term test.

2. Two cards are drawn from a deck of cards with replacement. Find the probability that: (a) The first card is an Ace and the second card is red. (b) Neither card has a value from (2, 3, 4, 5). 3. In the card game Black Jack your opponent receives a face-down card and a face-up card. In particular, you can see your opponents face-up card. This lends itself to conditional probability. For each question specify events E, and E, so that the give question is asking you to determine P(E|E2) and then answer the question. (a) What is the probability of that the face-down card is a 10, jack, queen or king, given that you see his face-up card is an ace? (b) What is the probability of that the face-down card is a 10, jack, queen or king, given that you see his face-up card is an ace and you know your own hand consists of a 4 and a 5? 4. Suppose that you buy a lottery ticket containing k distinct numbers from among {1,2,...,n} where 1 < k s n. To determine the winning ticket, k balls are randomly drawn without replacement from a bin containing n balls numbered 1,2,...,n. What is the probability that at least one of the numbers on your lottery ticket is among those drawn from the bin?