### Brain Teasers

# Odds of the Lottery

Assume a lottery is held where there are 5 winning numbers from 1 to 50 inclusive, and no number is repeated. Do you stand to make more money by picking your own numbers or having a computer give you random numbers?

### Hint

Try to pick some random numbers yourself.### Answer

You have better odds of making more money if you let the computer pick. If you have ever seen someone try to make random numbers, most people can't. If you are trying to pick random numbers, you will probably never pick 1-2-3-4-5 unless you are trying to make up for not picking numbers like that. However, a computer picking random numbers would likely pick that as much as the winning numbers would be that. So, your odds would be better to get the numbers from a computer because there would be less people to share the money with since the numbers are less easily reproduced.But, your odds of winning were never really good in the first place.

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## Comments

It doesn't matter if the numbers you pick are random or not. you have exactly the same chance of winning with whatever numbers you pick. It's equally likely for 1,2,3,4 & 5 to come out, as any other set of 5 numbers. So it doesn't matter who picks the numbers. Same odds. (Still not good odds though.)

andy's right.

It really makes you think- if there are the same chances of winning with the numbers 1,2,3,4,5 as any other numbers, it's better not to play the lottery...

Let me explane: It is very hard to pick numbers randomly yourself, and your mentality may never allow you to pick some numbers unless you aretrying to make up for not picking them (Which wouldn't be random), thus making a smaller pool of numbers to pick from, while a computer picks from the whole group, not just the pool.

Sorry, Mogmatt, but it doesn't make any difference where the 5 numbers come from - any group of 5 numbers have the same odds of winning as any other group of five numbers. Your argument of a computer using the entire number pool to choose from isn't valid - even if I use the same numbers every week, I have the same chance of winning as someone who uses a different random number every week. The odds are the same for everybody (unless of course you buy more tickets).

I agree with the sentiment that Mogmatt's logic is wrong. Indeed, any combination of 5 numbers has 1 in 2,118,760 chance of winning. IE: 1 in(50!/45!/5!).

However, if we assume that there are far more than 2,118,760 entries in the lotto, (say 100,000,000) then the method of choosing your numbers can affect the size of your potential prize. If you choose your own numbers and happen to win, you are more likely to need to share your 1st prize with more people who also chose their own numbers.

However, if we assume that there are far more than 2,118,760 entries in the lotto, (say 100,000,000) then the method of choosing your numbers can affect the size of your potential prize. If you choose your own numbers and happen to win, you are more likely to need to share your 1st prize with more people who also chose their own numbers.

Your odds are whatever 2,000000 to 1, this is because you only picked one set of numbers. For example, it doesn't matter if you don't like picking numbers 7-50, and pick your 5 numbers exclusively from 1-6, you still have one chance to 2 million of winning.

GOTO COLLEGE AND TAKE PROB AND STAT FOOL

There are some blonds in the wide world so if they let the computer pick they would not get messed up. No offense to hair color.

mogmatt is right. you have a better chance if you let the computer pick from all the numbers, instead of you picking some, because then it would be more widespread. because usually the lotto is not 14,15,16,17,18.

wwwwait i just read it again and i disagree with it now... it doesn't matter what the numbers you pick are, even if you pick from a 9 number pool. you could pick the last five numbers of your phone number or social security number or locker combonation and you would still get the same chance, so basically this question is unanswerable.

100% origional!, but flawed.

Dazza's right, although his comments apply

even if the number of entries is less than 2 million.

The odds of *winning* are unchanged no matter how

you pick your numbers, but the money odds are better

if you let the computer pick, because you are less likely

to have to share the prize if you win. Good puzzle, though

the explanation was a little unclear.

even if the number of entries is less than 2 million.

The odds of *winning* are unchanged no matter how

you pick your numbers, but the money odds are better

if you let the computer pick, because you are less likely

to have to share the prize if you win. Good puzzle, though

the explanation was a little unclear.

By the way, shouldn't this one have been under "Probability," not "Logic"?

Mogmatt is actually correct. If you ask a normal person to pick 5 numbers without ever looking at this teaser, you'll find out that the same couple of numbers will appear often. Good job Mogmatt.

This is more of an opinion answer. There really isn't an answer to this, becase you have the same chance of winning the lottery, then when the numbers are drawn.

wwwwait disregard my last comment

Wow, its hard to believe how little people know about probability. Like many have pointed out, it doesn't matter at all how any number is chosen in any lotery. Every number has the exact same odds of winning, even a number that won last week has the same odds of winning again as any other. Also if you want to get really picky you could say that even the computer generated numbers are not really "random". a computer needs a program or rule to follow in order to throw out an arbitrary number and if you know that rule and how it is used you could predict the number that the computer will generate thus making it non-random. In fact there is really no such thing true randomness because no matter how hard you try to make a series of random numbers there will allways be formula that will generate that same series and therfore predict the next number. There is also no mathematical definiton what a random series is exept for an unofficial one that states someting like if the formula that describes the series is longer than series itself then the series is random.

Some people just whine too much, I liked the teaser mog as it is orignal.

Dec 04, 2011

It supprises me how people do not understand this... Just because the probability is the same does not mean they are even... If the numbers you chose were chosen by others then you would not win as much money that is the point not probability...

Is it worth noting that even a computer is unable to produce true randomness? Is it even possible to measure whether something is "more random" than another, probability questions aside?

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