Interview Question

Trading Intern Interview Philadelphia, PA

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?
Answer

Interview Answer

9 Answers

1

Fair value is 5.5

2nd game:
FV = (3.5 x 5 + 6 + 7 + 8 + 9 + 10)/10 = 4.75

EASY! on Jul 16, 2012
0

You decide on taking the dollar value on the card or $3.50 *before* seeing the number on the card. And you get $5, if you open that card, not $0. So:

2nd game:

(1/2)*3.5 + (1.2)*(1/10*[5+6+7+8+9+10]) = 4

YouAreWrong on Aug 15, 2012
1

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.

There is not a 50% chance of selecting 3.5 @Your are WRong

@ EASY.
There is not a 10% chance of receiving $3.5 as numbers under 5 are worthless this will /should change your perspective.

FJM on Oct 2, 2012
0

FJM is correct. "Cards worth less than 5 are now valued at $0" - that does not include card number 5.

OP on Oct 2, 2012
0

how does 4.10 make sense if 4.5 is the ev of taking the card..ii think you are incorrect. can you explain your reasoning. using 1/10 to take your average and then multiplying by .6 seems like you are double counting

incorrect on Oct 9, 2012
9

Total amount=3.5*4+(5+6+~+10)
Expected value=total/10=5.9
@FJM no idea where your 4.5 coming from

xinzhuo on Oct 13, 2012
2

OK agreed with xinzhuo. Should be 7.5 instead of 4.5 in FJM's calculation, which gives 5.9.

OP on Oct 14, 2012
2

Agreed. I double counted.

3.5*.4 + 7.5*.6

3.5 was given

7.5 =(5+6+7+8+9+10)/6

FJM on Oct 14, 2012
0

"You decide on taking the dollar value on the card or $3.50 *before* seeing the number on the card."
2nd game:
Obviously, the game price should be no less than 3.5, otherwise there is an opportunity for arbitrage. Now that the price is higher than 3.5, it makes no sense for a rational player to choose just take 3.5 dollar and exist the game. The player should always choose to bet. And the expectation for betting is (5+6+...+10)/10 = 4.5.

Jay on Jan 19, 2015

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