Fred is giving away samples of dog food. He makes visits door to door, but he gives a sample away (one can of dog food) only on those visits for which the door is answered and a dog is in residence. On any visit, the probability of the door being answered is 3/4, and the probability that any given household has a dog is 2/3. Assume that the events “Door answered" and “A dog lives here" are independent and also that events related to different households are independent.

What is the probability that Fred gives away his first sample on his third visit?

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Given that he has given away exactly four samples on his first eight visits, what is the conditional probability that Fred will give away his fifth sample on his eleventh visit?

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What is the probability that he gives away his second sample on his fifth visit?

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Given that he did not give away his second sample on his second visit, what is the conditional probability that Fred will give away his second sample on his fifth visit?

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We will say that Fred “needs a new supply" immediately after the visit on which he gives away his last sample. If he starts out with two samples, what is the probability that he completes at least five visits before he needs a new supply?

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If he starts out with exactly 10 samples, what is the expected value of the number of homes with dogs where Fred visits but leaves no samples (because the door was not answered) before he needs a new supply?

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1)17/10

2)41/17
3)b/a

the right answers are:

1)1/8
2)1/8
3)1/8
4)1/6
5)5/16
6)10/3