(1) 5 points What is the probability that when a coin is flipped six times in a row, it lands heads up every time? (2) 10 points What is the probability that a five-card poker hand con- tains the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts? (3) 10 points What is the probability that a five-card poker hand con- tains at least one ace? (4) 10 points What is the probability that a five-card poker hand con- tains two pairs (that is, two of each of two different kinds and a fifth card of a third kind)? Section 7.2 Practice Homework: (1) 5 points What probability should be assigned to the outcome of heads when a biased coin is tossed, if heads is three times as likely to come up as tails? What probability should be assigned to the outcome of tails? (2) 10 points Find the probability of each outcome when a biased die is rolled, if rolling a 2 or rolling a 4 is three times as likely as rolling each of the other four numbers on the die and it is equally likely to roll a 2 or a 4. (3) 10 points A pair of dice is loaded. The probability that a 4 appears on the first die is 2/7, and the probability that a 3 appears on the second die is 2/7. Other outcomes for each die appear with probability 1/7. What is the probability of 7 appearing as the sum of the numbers when the two dice are rolled? (4) 10 points What is the probability of these events when we randomly select a permutation of {1, 2, 3, 4}? a) 1 precedes 4. b) 4 precedes 1. ) 4 precedes 1 and 4 precedes 2. d) 4 precedes 1, 4 precedes 2, and 4 precedes 3. e) 4 precedes 3 and 2 precedes 1. (5) 10 points Suppose that and F are events such that p(E) = 0.7 and p(F) =0.5. Show that p(EU F) > 0.7 and p(ENF)>0.2