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?

Answer 1

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_ix_i
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