Question

The Brady & Matthew Camera Company has just come out with their newest professional quality digital camera, the ToughPix 1. The company is selling this camera only through its new mobile app at a profit of $245 per camera. This purchase comes with a guarantee that, barring gross negligence, if the camera breaks in the first two years after purchase, Brady & Matthew will replace it free of charge. Replacing a camera in this way costs the company $3500. Suppose for each Toughpix 1 there is a 3% chance that it will need to be replaced exactly once, a 2% chance that it will need to be replaced exactly twice, and a 95% chance that it will not need to be replaced.

(If necessary, consult a list of formulas.)
If Brady & Matthew knows that it will sell many of these cameras, should it expect to make or lose money from selling them? How much?
To answer, take into account the profit earned on each camera and the expected value of the cost of replacements of the camera.
Brady & Matthew can expect to make money from selling these cameras.
In the long run, they should expect to make dollars on each camera sold.
Brady & Matthew can expect to lose money from selling these cameras. In the long run, they should expect to lose dollars on each camera sold.
Brady & Matthew should expect to neither make nor lose money from selling these cameras.?

Answer 1

To determine whether Brady & Matthew Camera Company will make or lose money from selling the ToughPix 1 cameras, we need to consider the profit earned on each camera and the expected value of the cost of replacements.

Let's calculate the expected value of the cost of replacements first. We know that there is a 3% chance of needing to replace the camera once, a 2% chance of needing to replace it twice, and a 95% chance that it will not need to be replaced at all.

To calculate the expected value, we multiply each outcome by its probability and sum them up:

(0.03 * 1 replacement) + (0.02 * 2 replacements) + (0.95 * 0 replacements) = 0.03 + 0.04 + 0 = 0.07

So, the expected value of the cost of replacements is 0.07 times the cost of replacing a camera, which is $3500:

0.07 * $3500 = $245

Now, let's consider the profit earned on each camera. The company sells each camera through its mobile app at a profit of $245 per camera.

Since the expected value of the cost of replacements ($245) matches the profit earned on each camera ($245), the company can expect to neither make nor lose money from selling these cameras in the long run.

Therefore, the correct answer is:

Brady & Matthew should expect to neither make nor lose money from selling these cameras.