Absorbing
Markov chains are used in marketing to model the probability that a
customer who is contacted by telephone will eventually buy a product.
Consider a prospective customer who has never been called about
purchasing a product. After one 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 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% chance 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 will
eventually purchase the product?
b
What is the probability that a low-interest prospective customer will
ever be deleted from the list?
c
On the average, how many times will a new prospective customer be
called before either purchasing the product or being deleted from the
list?
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