It is critical that you understand conditional reasoning in order to understand

Question

It is critical that you understand conditional reasoning in order to understand hypothesis testing. Conditional probability is a topic that you reviewed in your course Statistics for Business. The file "Conditional probability" on ICON will help you to refresh your knowledge of this topic. This homework set walks you through an important problem, but it's a hard problem. encourage you to work with others on this assignment. 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 pts Let's suppose we have a population of 100,000 people. How many of these people will buy your product? 100 How many people won't buy your product? 99000 Question 2 4 pts 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(LTBI 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)

Explanation / Answer

Answer to question# 1)

If total population is 100,000

Number of people who buy = 1% of 100,000

Number of people who buy = 1000

.

Number pf people who do not buy = 100,000 - 1000 = 99000

.

Question#2)

The firm is 90% accurate in identifying the people who buy the product

So if 1000 people buy the product the firm can identify = 90% of 1000 = 900 people

P(LBP | Buy) = 0.90

.

Similary the firm is 90% accurate in identifying the people who do not buy the product

Thus 90% of 99000 = 89100

Thus LTB = 99000 - 89100 = 9900

P( LTB | No buy) = 9900 / 99000 = 10%

.

Question# 3)

Total people the firm says will buy the product is : 900 + 9900 = 10800

P(LTB) = Number of LTB / Total number

P(LTB) = 10800 / 100000

P(LTB) = 0.108

.

Question# 4)

Total buyers and LTB = 900

.

P(LTB AND BUY) = 900 /100000 = 0.009

.

P(buy | LTB) = P( buy and LTB) / P(LTB)

P(Buy | LTB) = 900 / 10800

P(Buy | LTB) = 0.083

.

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