1. Fred is giving out samples of canned dog food. He makes calls door to door, but he leaves a sample (one can) only on those calls for which the door is answered and a dog is in residence. On any call the probability of the door being answered is 3/4, and the probability that any household has a dog is 2/3. Assume that the events "Door answered" and "A dog lives here" are independent and also that the outcomes of all calls are independent. a) Determine the probability that Fred gives away his first sample on his third call b) Determine the probability that he gives away his second sample on his fifth call. c) Given that he did not give away his second sample on his second call, determine the conditional probability that he will give away his second sample on his fifth call. d) We shall say that Fred "needs a new supply" immediately after the call on which he gives away his last can. If he starts out with two cans, determine the probability that he completes at least five calls before he needs a new supply. 2. A student's summer job is to call the university alumni for support for the university's scholarship fund. Studies indicate that the probability that each of the student's calls is answered is 1/3. What is the probability that the second call to be answered on one particular day is the student's sixth call? 3. The members of a Girl Scout troop are selling cookies from house to house in a suburban town. The probability that they sell a set of cookies (that is, one or more packs of cookies) at any house they visit is 0.4. i) If they visited eight houses in one evening, what is the probability that they sold cookies in exactly five of these houses? ii) If they visited eight houses in one evening, what is the expected number of sets of cookies that they sold? iii) What is the probability that they sold their third set of cookies in the sixth house they visited? 4. Defects occur along the length of a filament at a rate of 2 = 2 per foot. Calculate the i) Probability that there are no defects in the first foot of the filament. ii) Conditional probability that there are no defects in the second foot of the filament, given that the first foot contained a single defect.