Final answer:
The expected value of selecting an envelope from the box is $9.32, which is less than the $10 fee. Hence, this would not be a good deal as you would lose money on average.
Step-by-step explanation:
If a friend offers you the opportunity to select an envelope for a $10 fee, and you can receive a coupon for a free gift of varying values ($6, $8, $12, or $40), this situation involves calculating the expected value to determine if it's a good deal. To find the expected value (EV), you multiply the value of each outcome by its probability of occurring and then sum these products.
Here is the breakdown of the expected value calculation:
- Probability of $6 coupon = 10/100
- Probability of $8 coupon = 80/100
- Probability of $12 coupon = 6/100
- Probability of $40 coupon = 4/100
EV = (10/100 * $6) + (80/100 * $8) + (6/100 * $12) + (4/100 * $40)
EV = ($0.60) + ($6.40) + ($0.72) + ($1.60)
EV = $9.32
Since the expected value of $9.32 is less than the $10 fee to select an envelope, on average you would lose money on this deal.