Question

What is the expected gain or loss for the antique store owner when selling an antique china cabinet, considering a 45% chance of making $1200, a 50% chance of making $900, and a 5% chance of breaking even?

Answer 1

The expected gain for the antique store owner when selling an antique china cabinet, considering various probabilities for different gains, is calculated using expected value and results in a predicted profit of $990.

Step-by-step explanation:

To calculate the expected gain or loss for the antique store owner when selling an antique china cabinet with different probabilities for various outcomes, you would use the concept of expected value. The expected value is a type of weighted average of all possible outcomes, where each outcome is multiplied by its probability of occurrence.

The calculation for this scenario would be as follows:

• For the 45% chance of making $1200, the contribution to the expected value is 0.45 * $1200.
• For the 50% chance of making $900, the contribution to the expected value is 0.50 * $900.
• For the 5% chance of breaking even (making $0), the contribution to the expected value is 0.05 * $0.

The expected value (EV) is the sum of these contributions:

EV = (0.45 * $1200) + (0.50 * $900) + (0.05 * $0)

EV = $540 + $450 + $0

EV = $990

Therefore, the expected gain for the antique store owner when selling the antique china cabinet is $990.