You work for a firm that sells a product. The probability that any random person

Question

You work for a firm that sells a product. The probability that any random person wants to buy your product is 1%. A marketing firm claims that it will be 90% accurate in identifying the people who will buy your product and, also, 90% accurate in identifying the people who will not buy your product. They want to sell you the names of the people they have identified as potential buyers for $1 per name. Should you purchase $1000 names? Your product sells for $10.

How many total people did the firm say were "likely to buy" (LTB)?  

What is the probability of LTB, P(LTB)? Use three decimal places.

Let's suppose you decide to buy 1000 names at $1 per name. Thus, you spend $1000 on names. How many people in that group, on average, do you expect to buy your product?

How much money did you make or lose when you bought the names? If you made money, type in a positive number. If you lost money, add a negative sign before your answer. Do not use a dollar ($) sign.

Explanation / Answer

let A be the event that a random person wants to buy the product.

B be the event that the marketing firm identifies correctly whether a person will buy the product or not

then according to question

P[A]=0.01 so P[Ac]=0.99

P[B|A]=0.90 and P[B|Ac]=0.90

so P[LTB]=P[likely to buy]= P[A|B]=P[B|A]*P[A]/P[B] using Bayes' theorem

now P[B]=P[B|A]*P[A]+P[B|Ac]*P[Ac]=0.90*0.01+0.90*0.99=0.90

so P[LTB]=0.90*0.01/0.90=0.010 [answer]

so if you buy 1000 names at $1 per name then the expected number of persons in the group who wants to buy the product is 1000*P[LTB]=1000*0.01=10 [answer]

the product sells on $10 each

so expected amount of money you get by selling the product is $10*10=$100

but you have paid already $1000

hence you lost money of -900

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.