TNT is offering a million dollars to anyone who picks the top ten drivers – in order – at any of the six races they broadcast. You have up until 25% of the race has been run to lock in your selections, which means up to mile 100 at Daytona this weekend. How likely are you to win?
You have a 1 in 43 chance of picking the first driver correctly. There are now 42 drivers left and you have a 1 in 42 chance of picking the second driver correctly. When you calculate the probability of doing two things, you multiply the probabilities. It makes sense that there ought to be less probability of picking two numbers in a row than of picking one, right? So the odds of picking two drivers in the right order is 1 in (43 x 42) or 1 in 1,806.
Continuing this pattern…
# picked in right order
|Calculation||Chances are …|
|1||1 in 43||1 in 43|
|2||1 in (43 x 42)||1 in 1806|
|3||1 in (43 x 42 x 41)||1 in 74,046|
|4||1 in (43 x 42 x 41 x 40)||1 in 2,961,840|
|5||1 in (43 x 42 x 41 x 40 x 39)||1 in 115,511,760|
|6||1 in (43 x 42 x 41 x 40 x 39 x 38)||1 in 4,389,446,880|
|7||1 in (43 x 42 x 41 x 40 x 39 x 38 x 37)||1 in 162,409,534,560|
|8||1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36)||1 in 5,846,743,244,160|
|9||1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35)||1 in 204,636,013,545,600|
|10||1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34)||1 in 6,957,624,460,550,400|
That’s one in 6.9 quadrillion to get all ten in the right order.
Is Picking Them in Order Harder?
What if TNT had just said you had to get all ten, in no particular order?
If you look at ten numbers, there are ten ways of picking the first number, nine of picking the second, etc. That multiplies out to there being (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1=) 3,628,000 different ways of organizing ten numbers in every which way possible.
If TNT had decided that you only needed to get the drivers right, but not the order, your chances would increase to a whopping 1 in 1,917,334,783.
But there aren’t Really 43 Drivers Capable of Placing in the Top Ten…
OK, in reality, the odds are a little better. The calculation above assumes that the finish is a totally random event and we know that it’s not because there are 7-9 start and parkers. Realistically, you’re picking from maybe 35 cars (8 S&Ps), so the odds for getting all ten in the right order if you’re only picking from 35 drivers are 1 in 818,441,006,423,040. or 1 in about 818 trillion.
But there aren’t Even Really 35 Drivers Capable of Placing in the Top Ten…
Yeah, the husband tried to make the argument that you’re really only choosing from about 17 or maybe 20 drivers. Five words: Regan Smith and Trevor Bayne.
Just for comparison…
Odds of being struck by lightning are 1 in 576,000.
Odds of being killed by lightning are about 1 in 2,320,000
Odds of a meteor landing on your house: 1 in 182,138,880,000,000
So you’ve got a better chance of a meteor landing on your house than winning that million dollars.
Often for promotions like this (free televisions if it snows 10 inches on New Year’s Day!!), a company will take out an insurance policy. They’ll pay some amount of money to hedge against paying more. The people at the insurance company who figure out how much to charge them use these types of calculations to figure out the risk. I’m guessing TNT wouldn’t want to pay much of a premium because the odds are clearly in their favor. But it’s a great promotion.
Does this mean you shouldn’t play? Heck no – TNT isn’t charging you to enter, so get your best guess together and see if you can beat the odds.
Look at this cool project from Clemson and DuPont to take middle and high school teachers to the racetrack and teach them about science! Way to go, Tigers.
The probability of becoming a saint is estimated at about one in 20 million, but if you’re Jacques Villeneuve, the odds rise to one in a flying pig.
Gratuitous link to The NASCAR Insiders just because their Wednesday Q&A is always worth checking out – it is a blog I always learn something from!
Daytona this weekend – read all about drafting vs. bump drafting, why you’re likely to see two but not three cars drafting together, why NASCAR limits radiator pressure to try to keep the two-car draft to a minimum, and why drivers shift to the right to get air to the engine if they’re turning left. Or take a look at the Science of Speed video on drag and drafting.