Asked by Anonymous
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?
Answers
Answered by
MathMate
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]=Σp<sub>i</sub>x<sub>i</sub>
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
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]=Σp<sub>i</sub>x<sub>i</sub>
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.