Question

The Brady & Matthew Camera Company has just come out with their newest professional quality digital camera, the ToughPix1. The company is selling this camera only through its new mobile app at a profit of $329 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 $2400. Suppose for each ToughPix1 there is a 2% chance that it will need to be replaced exactly once, a 3% chance that it will need to be replaced exactly twice, and a 95% chance that it will not need to be replaced. 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?

Answer 1

The Brady & Matthew Camera Company would expect to lose $2373.68 from selling the ToughPix1 camera.

Step-by-step explanation:

To determine whether Brady & Matthew Camera Company will make or lose money from selling the ToughPix1 camera, we need to calculate the expected profit. The probability of a camera needing to be replaced once is 2%, so the profit for that scenario would be $329. The probability of a camera needing to be replaced twice is 3%, so the profit for that scenario would be 2 × $329 = $658. The remaining 95% of cameras don't need to be replaced, resulting in a profit of $0. Now we can calculate the expected profit:

Probability of replacement once: 2% × $329 = $6.58Probability of replacement twice: 3% × $658 = $19.74Probability of no replacement: 95% × $0 = $0

Summing up the profits, the expected profit for each ToughPix1 camera sold is $6.58 + $19.74 + $0 = $26.32. Since the cost of replacing a camera is $2400, the company would expect to make a profit of $26.32 - $2400 = -$2373.68 from selling each camera.