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A “friend” offers you the following “deal.” For a \(10fee, you may pick an envelope from a box containing 100seemingly identical envelopes. However, each envelope contains a coupon for a free gift.

• Ten of the coupons are for a free gift worth\)6.

• Eighty of the coupons are for a free gift worth \(8.

• Six of the coupons are for a free gift worth \)12.

• Four of the coupons are for a free gift worth $40.

Based upon the financial gain or loss over the long run, should you play the game?

a. Yes, I expect to come out ahead in money.

b. No, I expect to come out behind in money.

c. It doesn’t matter. I expect to break even.

Short Answer

Expert verified

(b) No, I should not play, I expect to come out behind in money.

Step by step solution

01

Given information 

There are100identical envelopes and have to pick one envelope cost of $10.

Each envelope contains a gift. They are:

Ten envelopes contain $6gift.

Eighty envelopes contain $8gift.

Six envelopes contain $12gift.

Four envelopes contain$40gift.

02

Explanation

X represents the net profit.

X
PX
X.Px
-4
10/100=0.10
-0.4
-2
80/100=0.80
-1.6
2
6/100=0.06
0.12
30
4/100=0.04
1.2
Total1
-0.68

As we can see, if we play this game, we will lose money, so I expect to lose money.

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