# youre a game expert a gambler asks you to convince him why/why not he should stop buying a ticket for the 6/55 lotto with a jackpot prize of?

200 million. you need to present him a mathematical explanation that is easy to understand involving the explanation of chances of winning

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• When you select your 1st number, you have 55 numbers to choose from, and...

...a 1 in 55 chance of picking the right one.

(Mathematically, 1 in 55 is represented by the numerical fraction 1/55 or 0.018182.)

When you select your 2nd number, you have 54 numbers to choose from, and...

...a 1 in 54 chance of picking the right one.

(Mathematically, 1 in 54 is represented by the numerical fraction 1/54 or 0.018519.)

When you select your 3rd number, you have 53 numbers to choose from, and...

...a 1 in 53 chance of picking the right one.

(Mathematically, 1 in 53 is represented by the numerical fraction 1/53 or 0.018868.)

When you select your 4th number, you have 52 numbers to choose from, and...

...a 1 in 52 chance of picking the right one.

(Mathematically, 1 in 52 is represented by the numerical fraction 1/52 or 0.019231.)

When you select your 5th number, you have 51 numbers to choose from, and...

...a 1 in 51 chance of picking the right one.

(Mathematically, 1 in 51 is represented by the numerical fraction 1/51 or 0.019608.)

When you select your 6th number, you have 50 numbers to choose from, and...

...a 1 in 50 chance of picking the right one.

(Mathematically, 1 in 50 is represented by the numerical fraction 1/50 or 0.020000.)

In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to multiply.

So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.

1/55 × 1/54 × 1/53 × 1/52 × 1/51 × 1/50 = 1/20872566000

So, at this point, your odds of winning are 1 in 20872566000. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 6 numbers can be written down, which for 6 numbers is 6! (6 factorial) or 720. Divide 20872566000 by 720 to account for this, to get 28989675.

In other words, there are 720 different ways that the 6 numbers you choose can be filled out on your lottery ticket--if you choose your 6 numbers correctly, any of these ways will make a winning ticket.

That's it! You have a

1 in 28,989,675

chance of winning the lottery jackpot.

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