Lottery Ticket Chance

Question

You need to pay one dollar to buy an instant lottery ticket. In this instant lottery game, you have 10% chance to win a one dollar bill and 5% chance to win a five dollar bill. You are interested in the expected payout which you will receive in a single play. (Note: Payout= prize-cost)

Answer 1

 

   10% = 0.1

   5% = 0.05

  

100% - 10% - 5% = 85% of losing

 

  Expected value = sum of  (    winnings * probability)

 

 

                        =    0 * 0.10   + 4 * 0.05 +   -1 * 0.85

 

                        =   0.2 - 0.85

 

                         = -0.65

 

because you have already paid $1 to play the game, so $1 is deducted

from any winnings. So winning $1 means you NET 0;

winning $5 means you NET $5.

So if you lose, you lost $1

 

 

In the long run, the expected value is that you will LOSE 65 cents