Math Problem Statement

You have a product you are trying to sell and you are considering purchasing online ads. The cost of the ad will be $0.14 each time it is shown. The price of your product is $17.50. Do the following for the given probability estimate: a) Find the expected value (to you) per ad that is viewed. b) Assume that you have an advertising budget large enough to place about 25,000 ads. Are the ads likely to be a good purchase? Explain. c) Would your answers to part (b) change if you could afford only 500 ads? Explain.

Solution

The problem in the image involves calculating the expected value and analyzing the effectiveness of an ad campaign. Let's break it down:

Part (a): Find the expected value (to you) per ad that is viewed.

The key information given is:

  • The cost of the ad per view is $0.14.
  • The price of the product is $17.50.
  • The probability of a purchase after someone sees the ad is 1 in 250 people (which is 1250\frac{1}{250}).

To calculate the expected value per ad view, you can use the formula for expected value:

Expected Value=(probability of purchase)×(profit per purchase)(cost per ad view)\text{Expected Value} = (\text{probability of purchase}) \times (\text{profit per purchase}) - (\text{cost per ad view})

Here’s how we can plug the values in:

  • Probability of purchase = 1250\frac{1}{250}
  • Profit per purchase = $17.50 (price of the product)
  • Cost per ad view = $0.14

Expected Value=(1250)×17.500.14\text{Expected Value} = \left(\frac{1}{250}\right) \times 17.50 - 0.14

Let me calculate this value for you.


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Math Problem Analysis

Mathematical Concepts

Probability
Expected Value
Cost-Benefit Analysis

Formulas

Expected Value = (Probability of purchase) × (Profit per purchase) - (Cost per ad view)

Theorems

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Suitable Grade Level

Grades 9-11