Business and Management 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?