Question

Exercise 4. Fred is giving out samples of 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. (1) Determine the probability that Fred gives away his first sample on his third call. (2) Given that he has given away eractly four samples on his first eight calls, determine the conditional probability that Fred will give away his fifth sample on his eleventh call (3) Determine the probability that he gives away (4) Given that he did not give away his second sample on his second call, determine the condi- tional probability that he will leave his second sample on his fifth call. (5) We will 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. 6) If he starts out with eractly m cans, determine the ezpected value and variance of Dm, the number of homes with dogs which he passes up (because of no answer) before he needs a his second sample on his fifth call new supply

Answer 1

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