Add a carnival, you play ring toss game 30 times. It's only a dollar to play, and your chances of winning the five dollar prize are advertised at 15%! What are your expected winnings?
Assuming probabilities work evenly for 30 times, then you would have won the $5 prize 30*0.15=4.5 times, with a total value of 4.5*5=$22.5 while paying $30 to play.
So your expected winning (for one play) is
22.5/30-$1=0.75-1=-$0.25
i.e.
you expect to lose 25 cents each time you play.
Note: playing 30 times might not give you the expected "winning", but perhaps 30,000 times might come close.
The mathematical equation for calculating expectations is:
E[x]=Σpixi
here
P(win)=0.15, P(lose)=0.85
x(win)=5-1=4, P(lose)=-1
E[x]=0.15*4+0.85(-1)
=-0.25
To calculate your expected winnings, we need to determine the probability of winning the five-dollar prize and the probability of losing.
Given that the chances of winning the five-dollar prize are advertised at 15%, we can say that the probability of winning is 0.15, or 15%. Consequently, the probability of losing is 1 - 0.15 = 0.85, or 85%.
Now, let's calculate your expected winnings:
- For each game, you pay one dollar to play.
- If you win, you receive five dollars.
- If you lose, you don't receive any money.
Since you play the game 30 times, the expected winnings can be calculated as follows:
Expected winnings (E) = (Probability of winning × Amount won per game) + (Probability of losing × Amount lost per game)
E = (0.15 × 5) + (0.85 × -1)
E = 0.75 - 0.85
E = -0.10
Therefore, your expected winnings are -0.10 dollars. This means, on average, you can expect to lose 10 cents per game over the course of 30 games.