Advertisements
Recent

[Brain Teaser] How much would you pay to play this game?

Question:

  1. You play a game where you earn the face value of the die ($1 if you roll a one, $2 if you roll a two, so on and so forth). If you can roll the die one time, how much would you pay to play this game?
  2. You play the same game but only this time, you have an option to roll one more time. How much would you pay to play this game?

 

 

Interview Questions

 

 

Answer:

  1. Because you have an equal probability of rolling 1, 2, 3, 4, 5, or 6, you need to find the expected payoff/value. Expected value is 3.5 or you would be willing to pay up to $3.50 to play this game.
  • (1)*(1/6) + (2)*(1/6) + (3)*(1/6) + (4)*(1/6) + (5)*(1/6) + (6)*(1/6) = 3.5
  1. If you roll a 4, 5, or 6 on your first roll, you would not roll again since your expected value on one roll is 3.5 (answer above). But if you roll a 1, 2, or 3, you would roll again. Therefore, you have 1/2 probability of not rolling and 1/2 probability of rolling again. Your “reroll” also has an expected value of 3.5. As rolling a 4, 5, or 6 is equally likely, the expected return is 5. Expected value on 2 rolls is the following: (5)*(1/2) + (3.5)*(1/2) = 4.25 or you would be willing to pay up to $4.25 to play this game.

 

Image Source: relativelyinteresting.com
Advertisements

Leave a Reply

Your email address will not be published.