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.

Question 1 (2 points)

Question 1 options:

Let's suppose we have a population of 100,000 people. How many of these people will buy your product?

How many people won't buy your product?

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Question 2 (4 points)

Question 2 options:

Of the 1000 people who would buy the product, how many will the firm indicate as "likely to buy" (LTB)?

In other words, what is P(LTB | Buy)?

Of the 99,000 who will not buy the product, how many will the firm indicate as "likely to buy" (LTB)?

In other words, what is P(LTB | No Buy)?

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Question 3 (2 points)

Question 3 options:

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.

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Question 4 (3 points)

Question 4 options:

How many total people are buyers AND LTB?

What, then is P(LTBBuy)? Use three decimal places.

P(LTBbuy)P(LTB)

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Question 5 (2 points)

Question 5 options:

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

1.

Let's suppose we have a population of 100,000 people. How many of these people will buy your product?

1% will buy. Hence,

1% of 100000 = 1000 will buy [ANSWER]

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How many people won't buy your product?

The rest won't buy, so

100000 - 1000 = 99000 won't buy [ANSWER]

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2.

Of the 1000 people who would buy the product, how many will the firm indicate as "likely to buy" (LTB)?

They will mark 90% of them, so

90% of 1000 = 0.90*1000 = 900 [ANSWER]

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In other words, what is P(LTB | Buy) = 0.90 [ANSWER, as is given]

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Of the 99,000 who will not buy the product, how many will the firm indicate as "likely to buy" (LTB)?

10% of them will be marked likely to buy, so

10% of 99000 = 9900 [ANSWER]

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In other words, what is P(LTB | No Buy) = 1 - 0.90 = 0.10 [ANSWER]

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