Textbook ExpertVerified Tutor
7 Nov 2021
Given information
A “friend” offers you the following “deal.” For a $10 fee, you may pick an envelope from a box containing 100 seemingly 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?
b. No, I expect to come out behind in money.
Step-by-step explanation
Step 1.
Let X= dollars in the following coupons which is in the envelope respectively
and p(x) = probability of getting envelope.
Here, we have only $10 to select an envelope that has a coupon,
- if a coupon is worth $10 then 10 envelopes will cost worth $100 which is a loss for me because we have to pay an extra $9
- if a coupon is worth $10 then 80 envelopes will cost worth $800 which is a loss for me
- if a coupon is worth $10 then 6 envelopes will cost worth $60 which is a loss for me.
- if a coupon is worth $10 then 4 envelopes will cost worth $40 which is a loss for me.
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