The question involves calculating the expected value of picking an envelope for a $10 fee with various gift values inside. After computing the expected values for each type of gift and adding them together, the total expected value is $9.32, which is less than the cost of the deal, suggesting it's not worthwhile.
The question seems to be about making a decision based on expected value in a scenario where a friend offers a deal involving picking an envelope from a box for a $10 fee.
Each envelope contains a coupon for a free gift with varying values.
To determine whether the deal is worthwhile, one must calculate the expected value of picking an envelope.
To calculate the expected value, you multiply the value of each outcome by its probability and then sum these values. Here are the calculations:
10 envelopes with a $6 gift: 10/100 * $6 = $0.60
80 envelopes with an $8 gift: 80/100 * $8 = $6.40
6 envelopes with a $12 gift: 6/100 * $12 = $0.72
4 envelopes with a $40 gift: 4/100 * $40 = $1.60
Add these expected values together to get the total expected value: $0.60 + $6.40 + $0.72 + $1.60 = $9.32
Since the expected value of $9.32 is less than the $10 fee to pick an envelope, mathematically, the deal is not beneficial.