Answer Happy

A company calls its potential customers to induce them to buy
their product. The company considers their customers to have no
interest, a low degree of interest or a high degree of interest of
buying the product. If a customer has no interest in buying the
product, then, after one phone call, there is a 60% chance that the
customer will express a low degree of interest in the product, a
30% chance of a high degree of interest, and a 10% chance that the
customer will be deleted from the company’s list of prospective
customers. Consider a customer who currently expresses a low degree
of interest in the product. After another call, there is a 30%
chance that the customer will purchase the product, a 20% chance
the person will be deleted from the list, a 30% chance that the
customer will still possess a low degree of interest, and a 20%
chace that the customer will express a high degree of interest.
Consider a customer who currently expresses a high degree of
interest in the product. After another call, there is a 50% chance
that the customer will have purchased the product, a 40% chance
that the customer will still have a high degree of interest, and a
10% chance that the customer will have a low degree of
interest.
a) What is the probability that a new prospective customer (the
one that right now has no interest in buying the product) will
eventually purchase the product? (8 pts)
b) What is the probability that a low-interest prospective
customer will ever be deleted from the list? (8 pts) (Four
decimals)
c) On the average, how many times will a new prospective
customer (the one that right now has no interest in buying the
product) be called before either purchasing the product or being
deleted from the list? (9 pts)