To solve this problem, we need to calculate the expected cost of replacing the ToughPix1 camera and compare it to the profit made from each sale.

Step 1: Calculate the expected cost of replacements.

Given:

• There is a 5% chance that a camera will need to be replaced once.
• There is a 2% chance that a camera will need to be replaced twice.
• There is a 93% chance that the camera will not need to be replaced.
• The cost of replacing a camera is $4,600.

We calculate the expected cost of replacement using the formula: $\text{Expected cost} = (0.05 \times 4600) + (0.02 \times 2 \times 4600) + (0.93 \times 0)$ Breaking it down:

1. $0.05 \times 4600 = 230$ (for one replacement).
2. $0.02 \times 2 \times 4600 = 184$ (for two replacements).

Adding these together gives the total expected cost: $230 + 184 = 414 \text{ dollars}$

Step 2: Calculate the net profit per camera.

The profit from selling each camera is $308.

Subtract the expected replacement cost from the profit: $308 - 414 = -106 \text{ dollars}$

This result indicates that, on average, Brady & Matthew will lose $106 on each camera sold.

Conclusion

The correct answer is:

• Brady & Matthew can expect to lose money from selling these cameras. In the long run, they should expect to lose $106 on each camera sold.

Would you like more details on any step or have any questions?

Related Questions:

1. How would the expected cost change if the probability of one replacement increased to 10%?
2. What would happen to the net profit if the replacement cost decreased to $3,000?
3. How can Brady & Matthew reduce the expected losses on the camera sales?
4. What if the profit per camera was increased to $500? Would they still incur a loss?
5. How does changing the probabilities of replacement impact the expected cost?

Tip:

Always account for the probabilities of events happening when calculating expected values in business scenarios. This helps in making more informed decisions.