Real-Life Math
You've just been hired to drive in a series of 15 races for the Shmoe Team. They have great cars and the team is experienced.
Each race offers a purse of $20,000 to the winning team. Unlike most series, this race has no awards for 2nd or 3rd place. It's either win or lose.
In writing up the contract between you and the owner, the 2 of you have to agree on how much of the purse you get to keep for yourself, if you should happen to come in 1st in any of the races.
The team has offered you 2 options:
Option 1 pays $2,500 per race, whether you win or lose, and 10 percent of the purse if you should win.
Option 2 pays $600 per race, and 20 percent of the purse if you should win.
Since there are 15 races, you'll have to figure out your total earnings for the series. The thing is, you have no idea how many races you will win. You have, however, looked at who you will be racing against, what the tracks will be like, and how together the rest of the team is.
From this, you estimate that your odds of winning a race are 1 in 7. That means you figure you will win 1 out of every 7 races.
So, calculate your earnings for both options, assuming you will win all 15 races. Then calculate your earnings for both options, based on your 1 in 7 estimate. You'll want to take the option that pays the most if you only win the 1 out of 7, because chances are slim that you'll win every race.