4-9. Exercises
Ex 1. A class consists of 12 male and 8 female students. Students are chosen one-after another without replacement at random from the class.
What is the probability that the fourth male is selected as the seventh student chosen?
How many students would one expect to have to choose in this way in order to select a fourth male student?
Ex 2. A small herd of cows includes 3 having a certain disease and 15 that do not.
In randomly selecting and testing cows in this herd for the disease, what is the probability that all of the diseased cows will have been selected by the eighth selection, but not before? Suppose this process of selecting and testing cows until the third diseased one is found had to be repeated on many herds of 18 cows each of which contained 3 with the disease.
What are the mean and standard deviation of the numbers of cows that would have had to be selected in order to have selected the third cow having the disease?
Ex 3. A game is played as follows. A person draws cards at random without replacement one-after-another until a second Face card is obtained.
What is the probability that the person will draw exactly 5 cards from the deck?
What is the expected number of cards that the person would have to draw?
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