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A Cable Television Company Has Randomly Selected a Sample of 222

question 69

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A cable television company has randomly selected a sample of 222 Basic package customers for a marketing test to see which customers are more likely to upgrade to the Premium package. They monitored two predictor variables based on customer activity during the most recently billed month. Then they included a special upgrade offer for the Premium package along with their bill. The response variable Upgrade equals True if a customer accepted the offer to upgrade to the Premium package and equals False otherwise. The predictor variable ViewTime is the average daily minutes the customer had at least one TV on in their house. Network is 1 if the TV is tuned to a traditional ("over the public airwaves") broadcast network at least 50 percent of the time that it is turned on and 0 otherwise. Let the events U, Uc, HV, and NV denote the events that the randomly selected Basic customer, respectively, upgraded, did not upgrade, had a high ViewTime [a view time greater than the median amount of 507 minutes], and was primarily a traditional broadcast network viewer [i.e., spent at least 50% of time tuned to a traditional network]. The data they collected show: 1) 43 out of 222 Basic customers upgraded, or P(U) = 43/222.
2) 179 out of 222 Basic customers did not upgrade, or P(U_c) = 179/222.
3) 37 out of 43 upgraders had a high ViewTime, or P(HV|U) = 37/43.
4) 63 out of 179 non-upgraders had a high ViewTime, or P(HV|U_c) = 63/179.
"5) 7 out of 43 upgraders was primarily a traditional broadcast network viewer,
Or P(NV|U) = 7/43."
"6) 52 out of 179 non-upgraders was primarily a traditional broadcast network viewer,
Or P(NV|U_c) = 52/179.
Using naive Bayes' Theorem, what is the approximate probability that a Basic customer will upgrade if they do not have a high ViewTime and do not primarily view traditional broadcast networks?"

Definitions:

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Total Revenue

The total income generated from the sale of goods or services, calculated by multiplying the price by the quantity sold.

Demand Function

A mathematical equation that describes the relationship between the quantity of a good demanded and its price, as well as other factors like income and prices of related goods.

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The ratio reflecting the responsiveness of the quantity demanded or supplied of a good to changes in its price.