The Sweet Leaf Iced Teas Company is sponsoring a conventional bottlecap sweepstakes game. Under each bottle cap there is a note saying either “You are not a winner,” or the prize awarded. Suppose there are 20 of the game bottles on a shelf in the supermarket, and two of them are winners. A customer randomly selects six bottles from the shelf.
a. What is the probability of selecting no winning bottles?
b. What is the probability of selecting both winning bottles?
c. What is the mean number of winning bottles selected?
d. How many bottles would the customer have to purchase in order to expect one winning bottle?
There are over 1 million earthquakes worldwide of magnitude 2–2.9 each year. However, the mean number of earthquakes of magnitude 8 or higher is approximately one per year.38 Suppose a random year is selected.
a. What is the probability of exactly two earthquakes of magnitude 8 or higher?
b. What is the probability of at most four earthquakes of magnitude 8 or higher?
c. Suppose there are three earthquakes of magnitude 8 or higher. Is there any evidence to suggest that the mean is different from one? Justify your answer.
Managers at CafePress acknowledge that a variety of errors may occur in customer orders received via telephone. A recent audit revealed that the probability of some type of error in a telephone order is 0.20. In an attempt to correct these errors, a supervisor randomly selects telephone orders and carefully inspects each one.
a. What is the probability that the third telephone order selected will be the first to contain an error?
b. What is the probability that the supervisor will inspect between two and six (inclusive) telephone orders before finding an error?
c. What is the probability that the inspector will examine at least seven orders before finding an error?
d. What is the probability that the first error will be on the fourth telephone order or later? e. Suppose the first four telephone orders contain no errors. What is the probability that the first error will be on the eighth order or later?