Question

you open the first envelope, note that it contains the amount x, discard it and take the next amount which is larger than x

Answer 1

The question is asking you to find the expected value of the coupon you will select from a box of 100 envelopes.

Step-by-step explanation:

This question pertains to probability. To solve it, you need to consider the different probabilities of selecting each coupon value. Let's see the steps:

1. There are 100 envelopes in total, so the probability of selecting any specific envelope is 1/100.
2. The probability of selecting a $6 coupon is 10/100 because there are 10 of them.
3. The probability of selecting an $8 coupon is 80/100 because there are 80 of them.
4. The probability of selecting a $12 coupon is 6/100 because there are 6 of them.
5. The probability of selecting a $40 coupon is 4/100 because there are 4 of them.

Based on these probabilities, the question is asking you to find the expected value of the coupon you will select. To do this, you need to multiply each coupon value by its respective probability, and then sum these products. Let's calculate the expected value:
(10/100) * 6 + (80/100) * 8 + (6/100) * 12 + (4/100) * 40 = 0.6 + 6.4 + 0.72 + 1.6 = 9.32.

Therefore, the expected value of the coupon you will select is $9.32.