To maximize the probability that customers purchase products during a visit to a

ID: 3331717 • Letter: T

Question

To maximize the probability that customers purchase products during a visit to a website, a company that provides marketing services and website management experiments with different offers and website design to understand customer Web behavior. Possible actions by the website include offering the customer an instant discount, offering the customer free shipping, or doing nothing. A recent experiment found that customers make purchases 7% of the time when offered the instant discount, 5% when offered free shipping, and 2% when no special offer was given. Suppose 30% of the customers are offered the discount and an additional 40% are offered free shipping. Complete parts a through c. a) Construct a probability tree for this experiment. Complete the probability tree below Purchase--Discount and Purchase -Discount and No Purchase Discount NO Purchase-I Free Shipping-OCNP Purche-O-Shipping and Purchase - Shipping and No Purchase Purchase--Nothing and Purchase Nothing-FX No Purchase Nothing and No Purchase -O (Type integers or decimals.)

Explanation / Answer

Boxes of first columns:

From the given information we have,

P(discount) = 0.30

P(free shipping) = 0.40

P(nothing) = 1 - P(discount) - P(free shipping) = 0.30

Boxes fo second column:

P(purchase| discount) = 0.07

P(purchase | free shipping) = 0.05

P(purchase| nothing) = 0.02

By the complement rule,

P(not purchase| discount)=1-P(purchase| discount) = 0.93

P(not purchase | free shipping)=1-P(purchase | free shipping) = 0.95

P(not purchase | nothing) =1- P(purchase| nothing) = 0.98

Third column boxes:

P(purchase and discount) = P(purchase| discount)P(discount) = 0.07 * 0.30 = 0.021

P(purchase and free shipping) = P(purchase | free shipping) P(free shipping)= 0.05 *0.40 = 0.020

P(purchase and nothing) = P(purchase| nothing) P(nothing) = 0.02 * 0.30 = 0.006

P(not purchased and discount) = P(not purchase| discount)P(discount)= 0.93*0.30 = 0.279

P(not purchase and free shipping) = P(not purchase | free shipping)P(free shipping)= 0.95 * 0.40 = 0.38

P(not purchase and nothing) = P(not purchase | nothing)P(nothing) = 0.98 * 0.30 = 0.294

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