You need to show your work (formula setup, calculations, etc.) and state any properties or rules you need to solve the problems.

1) Should you use the binomial distribution? In each of the following situations, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. If a binomial distribution applies, give the values of n and p.

(a) You toss a fair coin until a tail appears. X is the count of the number of tosses that you make.

(b) Most calls made at random by sample surveys don't succeed in talking with a person. Of all calls to New York City, only one-twelfth succeed. A survey calls 500 randomly selected numbers in New York City. X is the number of times that a person is reached.

(c) You deal 10 cards from a shuffled deck of standard playing cards and count the number X of black cards.