Brain Teaser question Expected Value
Here is a question I found. There are posted answers but none of them seem to really make sense. Ill post the question, the answers given and what I think.. does anyone know for sure the correct answer
question:I have 10 cards face-down numbered 1 through 10. We play a game in which you choose a card and I give you the corresponding dollar amount. a) What is the fair price of this game? b) Now, after picking a card you can either take the dollar value on the card or $3.50. Also, cards worth less than 5 are now valued at $0. What is the maximum price you are now willing to pay for the game?
Answers people given: 3.5(.4) + (4.5)*.6 = $4.10
3.5 because this is what 40% will select, 4.5 as this is the avg of 5-10*1/10.
What I'm thinking is there is a 40% chance to get a 1 2 3 or 4 which would equal value $3.50 and a 60% chance to get a 5 6 7 8 9 or 10. so i would think the answer is 5.9 .. it seems like the second iteration should be worth more than the standard first one but these people are saying its not
A). The average of 1-10 = 5.5, which is the fair value
B). Not sure I understand the wording if the question. I assume you can't turn the card over before accepting the 3.5 dollar offer. Also, assume it is less than 5, not less than or equal to 5. If true, I would answer it like this: 5+6+7+8+9+10 = 45/10 = 4.5 (if the assumption is cards less than or equal to 5, then the expected value is 4). Either way, you would never take the offer of 3.5 (unless you were a giant pussy and assumed you couldn't play the game more than once, I guess).
If you can turn the card over and decide if you take the offer after seeing the card, then it would look like this: 3.5+3.5+3.5+3.5+5+6+7+8+9+10 = 59/10 = 5.9.
However, that would be a weird way to ask an interview question. I would expect the point of the question to be able to compare whether you should take the certain 3.5 or take the gamble for a certain expected value of either 4.0 or 4.5, depending on the actual wording of the question..
ok i see what you are saying about the first part of b.. i assumed the question was asked what would u pay for a game where under 5 becomes 3.5 else the same.. i guess how the wording should be is.. under 5 is zero rest the same.. you have an option of choosing the 3.5 flat payout before flipping do you flip so i see what you are saying now thanks!.. actually really easy i guess the poster just worded it weird
so basically the guy who is saying the answer is $4.10 is wrong i assume? The op said he was correct in staying 5 is not worth zero.
Answers people given: 3.5(.4) + (4.5)*.6 = $4.10
3.5 because this is what 40% will select, 4.5 as this is the avg of 5-10*1/10.
That makes no sense to me.. it seems like hes double counting using 1/10 to find the average of 5-10 and then multiplying it by 60%
thanks
The problem is that a few details are missing from the problem. You're not told whether or not you see the value of the card before you choose the $3.50 or the card. If you do see the value beforehand, the problem is really simple. If you don't, then you need some sort of criteria for choosing. Also, if you choose the card and it turns out to be worth $0 then your opportunity cost is -$3.50. If you always choose the card instead of $3.50 then your EV = (-3.5-3.5-3.5-3.5+5+6+7+8+9+10)/10=$3.10. If you always choose the $3.50 then EV = (3.5+3.5+3.5+3.5-1.5-2.5-3.5-4.5-5.5-6.5)/10=-$1. If you flip a coin to decide, then EV = $1.05. That's how I interpret the problem. It'a vague.
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