# May the Likelihoods Be Mostly in Your Favor

This is Prithi, the fifth grader, with another blog post, on probability. This title was inspired by Effie Trinket, in the Hunger Games.

Let’s say you buy a lottery ticket.You either win or lose. You figure that the chances are 50-50. What you don’t understand is that the chances are not 50-50. But you may ask: Isn’t it like a coin toss? The answer is no.

The explanation:

Let’s say the lottery ticket you buy is numbered from one to twenty. On drawing night, they pick one of the twenty numbers, and if you bought that ticket, you win. Otherwise, you lose.

Here’s a sample space for this problem:

{lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, win}.

Only one out of the twenty options can win. Win or lose are the two states you may find yourself in, but you are more likely to lose than win. The lottery tickets that we buy are not numbered from one to twenty, but have six numbers, from one to forty-two. They don’t pick one number, but six to find the winner. That means the chances are {lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose…

, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose, lose…

Oh, I can’t put a win anywhere here, because the chances of losing keep on going}

This is how the math will work: 1/42*1/41*1/40*1/39*1/38*1/37, or 0.000000000264763.

Therefore, the next time you buy a lottery ticket, don’t figure your chances are 50-50, and always make sure the likelihoods are mostly in your favor.