Question

X Section 5.8 Exercise 13 EQuestion Help 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 No Purchase - Discount and No Purchase Shipping and Purchase Free Shipping No Puchase -Shipping and No Purchase Purchase -Parchase -Nothing and Purchase Nothing -No Purchase - Nothing and No Purchase (Type integers or decimals.)

Answer 1

part a)

30% of the customers are offered the discount

The probability that a customer is offered the discount is 0.30

P(Discount) = 0.30

40% are offered free shipping

The probability that a customer is offered free shipping is 0.30

P(Free Shipping) = 0.40

The remaining would have been offered nothing

The probability that a customer is offered nothing is

P(Nothing) = 1- (0.4+0.3) = 0.3

We can fill in the first set of probabilities

a) Construct a probability tree for this experiment. Complete the probability tree below. Purchase -Discount and Purchase 0.30 Discount No Purchase - Discount and No Purchase Purchase Shipping and Purchase -Free Shippi0.40 -Shipping and No Purchase No Purchase - Purchase - Nothing and Purchase Nothing 0.30 -No Purchase Nothing and No Purchase (Type integers or decimals.)

Customers make purchases 7% of times when offered the instant discount is same as

The probability that a customer makes a purchase given that the customer is offered Discount is 0.07

P(Purchase Discount) 0.07

The probability that a customer makes no purchase given that the customer is offered Discount is

P(No Purchase Discount) = 1- P(Purchase Discount) - 1-0.07-0.93

Customers make purchases 5% of times when offered free shipping is same as

The probability that a customer makes a purchase given that the customer is offered free shipping is 0.05

P(Purchase Free Shipping) 0.05

The probability that a customer makes no purchase given that the customer is offered Free Shipping is

P(No Purchase Free Shipping) 1- P(Purchase Free Shipping) =1-0.05-0.95

Customers make purchases 2% of times when offered Nothing is same as

The probability that a customer makes a purchase given that the customer is offered Nothing is 0.02

P(Purchase Nothing) 0.02

The probability that a customer makes no purchase given that the customer is offered Free Shipping is

P(No Purchase Nothing) 1 - P(Purchase | Nothing) - 1-0.02 0.98

We can fill in the boxes int he second column

Purchase 0.07-Discount and Purchase 0.30No Discount No Purchase0.93-Discount and No Purchase Purchase O.05 Shipping and Purchase -Free Shippin0.40 -No Purchase O.95-Shipping and No Purchase -Parchase 0,02 Nothing and Purchase Nothing 0.30 No Purchase O.98 Nothing and No Purchase (Type integers or decimals.)

Finally we calculate the joint probability using the formula for conditional probabilities

We now fill in the last column

P(Purchase Discount P(Purchase Discount) P(Discount) 0.07 x 0.30 0.021 P(No Purchase | Discount) P(Discount) P(Purchase n Free Shipping) P(Purchase | Free Shipping) P(Free Shipping) 0.05 x 0.40 0.02 P(No Purchasen Free Shipping) P(No Purchase | Free Shipping) P(Free Shipping) 0.95 x 0.40 0.38 P(No Purchase n Discount) 0.279 = 0.93 x 0.30 P(Purchase Nothing) P(Nothing) 0.02 x 0.30 0.006 P(No Purchasen Nothing) P(No Purchase Nothing) P(Nothing) 0.98 x 0.30 0.294 P(Purchasen Nothing)

a) Construct a probability tree for this experiment. Complete the probability tree below. 0,021 Purchase 0.07-Discount and Purchase 0.30 Discount No Purchase0.93-Discount and No Purchase 0.279 -Purchase .05 0.02 Shipping and Purchase - Free Shippin0.40 O.38 No Purchase O.95-Shipping and No Purchase Purchase 0,02 Nothing and Purchase -0006 Nothing 0.30 No Purchase 0.98 Nothing and No Purchase .294 (Type integers or decimals.)