Question

A regional automobile dealership sent out fliers to prospoctive customers indicating that they had aleady won one of free dffocent prizes: an automobile valuad at \( \$ 20.000 \), a \( \$ 150 \) gas c"

A) $170,000.
B) $20,150.
C) $20,000.
C) $150.

Answer 1

The expected value of participating in a game where you pick an envelope after paying a $10 fee can be calculated using the probability and the prize for each kind of envelope. This calculation helps determine if the game is financially advantageous. It considers the costs and the likelihood of each possible outcome.

Step-by-step explanation:

When considering whether to participate in a promotional game, it's essential to understand the expected value of the proposition. Using the information provided, we can calculate the expected value for picking an envelope after paying a $10 fee. The expected value (EV) is the sum of the values of each possible outcome, each multiplied by its probability of occurring.

The calculation process would look like this:

• 10 envelopes with a $6 prize each, the probability = 10/100
• 80 envelopes with an $8 prize each, the probability = 80/100
• 6 envelopes with a $12 prize each, the probability = 6/100
• 4 envelopes with a $40 prize each, the probability = 4/100

EV = (10/100 * $6) + (80/100 * $8) + (6/100 * $12) + (4/100 * $40) - $10 (the cost to play)

Thus, the expected value will help to determine if the game is worth playing in financial terms. A positive expected value indicates a potentially profitable game, while a negative expected value suggests a loss over time.