Finding the Probability of Winning the Texas Lottery

[MiekWave]

So If I was an evil millionaire with 25.8 Million dollars and I purchased 25.8 Million tickets with a 1 in 1 chance of winning a jackpot of say, 51.6 Million, I would win $25.8 million back twice!

[patrickJMT]

@MiekWave people actually did this; the jackpot was larger than the number of tickets so they tried to buy all possible combinations, however, they ran out of time. they still did manage to get the winning ticket though.

[hydrobot2003]

Can't win if you don't play. Someone will eventually win. It happens all the time. :-)

[patrickJMT]

@hydrobot2003 yes, just not to you

[IsraeliXdude]

What is probability of you winning lotto in Texas and while going to collect your prize you are struck by lightning?

[patrickJMT]

@IsraeliXdude well, those are independent events, so you would multiply the individual probabilities together

[latinluigi]

What are my odds? Haha

[patrickJMT]

@latinluigi well, odds are different than probabilities

[wynz24]

@patrickJMT what are the evens?

[latinluigi]

What about the powerball draw tonight? It's at 245 million now and you have to pick 5 #s plus the two other power play #s

[Thedudethanksyou]

It was once put that you would win the lottery once every 40,000 years so just play for 40,000 years so you can win it.

No one here would be able to handle it if they won.

[Steve2323ZX]

The texas lotto has 54 balls and players have to pick which 6 will be drawn. The odds of winning with one ticket is 1 out of 25.8 million

[EnigmaticNeurosis]

There is a lesson to learn here: do not play the lottery unless you have been struck by lightening.

[damnd1907]

Funny, I don't hear people being struck by the lightning every other week?!

[patrickJMT]

@damnd1907 and your point is... ?

[gnyhwy]

@damnd1907 I would like to see a mathematical answer for that, but the simple rational to me would be that there are much more people attempting to win the lottery than there are attempting to get struck by lightning. LOL.

[patrickJMT]

@gnyhwy that sounds about right to me.... not to hard to figure out : )

[foxygermangirl123]

haha i like this kind of math :) where theres actually a chance to win something lol.

[Fugiman85]

I wish I could win the lotto.

[IsaacDyt]

thanks alot- i used your model to work out the probability to win the euromillions tonight! its a 80 million pound rollover! We have 5 balls 1-50 then two "special" balls 1 to 11

its a bit easier than yours 0. 000 000 008 581 but i think I'm still gona need a lot of luck!!

[Krinordh]

LOL, this is what I just learned at school :P

[mmtna]

a few moths back someone in my city won it I was pissed

[metallicgoth]

LEFTY! :D

[bubaabaa]

Well...you have to play to have a chance..and I think the best way to go is quick pick...most of the winners in history almost always played quick pick... and if its your destiny, then you might win...

[patrickJMT]

@bubaabaa lol

[jimmyz512]

@gix500

Its 1 over (36 factorial divided by (29 factorial times 7 factorial))

which =

1/8,347,680

= approximately 0.00000011979

[gix500]

in the danish lotto you have 36 numbers and have to hit 7 of them(any order) so whats the odds there???im guessing 1 in 10 mill or something, just a wild guess

if you say 36x36x36x36x36x36x36 the number becomes too big doesent it, because thats any combinations also with the same numbers twice or more

[unclepoepoe]

If i buy 56229 lottery tickets the odds suddenly swing in my favor for me winning the lottory and not gettting hit by lightning!!!!!!!!! WOOOOOOOOOOOOOO

[its123baby]

1 out of 2 billion chance of winning. So you're saying I have a shot?

[patrickJMT]

@its123baby yep, you sure do

[yingdiskette]

@patrickJMT I believe 123baby was just being sarcastic.

[patrickJMT]

@yingdiskette okie dokie.

[jaarmen3]

or it can be looked at as the probability of winning the texas lottery: your chances of going outside and falling into a volcano are more likeley to happen that winning a full lottery draw.

[logicpower6]

texas million = ballss... pick 5 ballss.. pick balls in any order... pick a different colour ball... original ball... special ball... how about you pick my balls... what are the chances in that.

[TheMishu1982]

nice

[jiro32]

are you off by one number? i came up with .00000000569 (8 zeros, not 9 zeros preceding the 569)... 1 / 175,711,536 = 5.691 X 10 ^ -9

[Uqload]

@jiro32 actually, he's correct, sorry :/

[jiro32]

@Uqload actually, I still think he's off by one zero, sorry :/

[llorkcir2]

You've got my vote. You're an excellent teacher, and I think you'd make a lot of complicated probability problems clearer to people studying for the exams. I'd spread the word about you at my school's actuarial club if you posted something.

[jws54]

the odds are written on the back of the ticket

[llorkcir2]

Do you do any tutoring for actuarial exams?

[patrickJMT]

@llorkcir2 i have thought about making some; was not sure anyone would be interested

[ARNRF67]

If you choose 5 numbers from 1 to 56, first multiply 1*2*3*4*5 and get 120, now multiply 56*55*54*53*52 and get 458,377,920 now divide that by 120 and get 3,819,816 now multiply that times 46 and get 175,711,536 and your odds of winning are 1 in 175,711,536

[ELTURBOMAN]

I figure you have the same chance of winning the lottery wether you play or not.

[FrozenInThyme]

Here in Florida the lighting chance is alot easier. :)

[TheCrazyFinn]

I wonder if there's a way to make winning more likely, like the equivelant of flying a kite in a thunderstorm! :)

[Victorinox99]

You're a hero.

[rajooah]

hey guys i did some research to see whether those numbers that were guessed on this video had actually come up any where as winning numbers, and i found out something very interesting. ON THURSDAY 1ST OF OCTOBER 2009, DRAW NO.698 AUSTRALIAN POWERBALL- 25 17 8 32 9 POWER BALL 17, DIVISION 1 PRIZE OF $4,930,63.15.......IF ONLY I WAS WATCHING THIS VIDEO THE NIGHT BEFORE THE DRAW!!!!

[fateindustry]

watch 25, 17, 8, 32, 9 ::: and 17 will come up. Then it will be ROFL.

[WhackaJacka]

So the calculation should be

56x56x56x56x56x46?

But if you pick one number each time that cannot be used again it should be

56x55x54x53x52x46?

[cabronian1337]

we left handers rulez

[Ramiromasters]

Pretty sure if every person in US would buy a ticket for sure someone would win.

Lets see .00000000056911 x 300,000,000 (US population) = .01707.... wow that is one percent chance! how come someone win every month?

[xSirFarisx]

Lol! :D somebody gotta WIN !!

[patrickJMT]

@xSirFarisx yep, might as well not be you

[NoorKaya]

i did not understand nothing actually , im into this and new to it too , and want to try my luck can u help me with some more explanations? my ya hoo email is Nizaleo please contact me , please

[lChupacabra]

The value of winning the lottery is less for you than the rest of us because you aren't smart enough to know what to do with your money if you did win. I'd recommend you not play the lottery.

[trevdrummer12]

Donated. Thanks!

[aizik2005]

Hello sir.

should not it be then

1/(56!) * 1/(55!) * 1/(54) * 1/(53) * 1/52!

because the propability of getting next wanted number increases as number of balls gets smaller. then all previous numbers * 1/46 or w/e it is.

or, if there are random numbers on a lottery sheet, then (5C5)/(56C5) * 1/46 makes sense

[FemmePhobia]

@aizik2005 i kind of agree with you and i think that in the video he solves the problem thinking that they extract the 5 balls at the same time....

[aizik2005]

@FemmePhobia

probably, but i forgot almost everything about probabilities =((

[StreetBalla705]

LMFAOOOOOO HAHA

[yanomandin]

ok, you said that there is a little chance to win a texas loto, I've been wonder why there is a proclaim winner every draw? could you imagine that

[AbyssZomG]

A LOT of people buy the tickets, some may buy more than 1 ticket too.

So if 1 million people buy tickets, then the probability of ANY one of those people winning would increase to 0.00056911

[lChupacabra]

Not sure what you mean by "proclaim winner" but there isn't a jackpot winner every draw. More often than not, noone wins the jackpot.

[frecklefacedawn7]

PatrickJMT....You have saved me for today, and probably tomorrow too. You are a HERO! Thanks bunches! Muah!

[chocolatecookie77]

i luv u, thanx ur great!

[MathMikie]

even tho it's much smaller than the lightning the lightning is still very small as well it's unlikey that either would ever happen to you

[patrickJMT]

yep, fo sho : )

i am not expecting either to happen to me

[billtruttschel]

You have one too many zeros in your calculation.

[XPAC03]

Thank you for making these videos, they help a lot. Just one question, what is a factorial?

[fireblade9001]

Factorial is nothing but multiplication.

i.e 56! = 56x55x54x53x52x51x50..........­.......x1

therefore the value of 56! is divided by 51! and 5! and then it is multiplies and subtracted with 1/46 then you get the figure.

Hope this helps. to be honest its a hell lot os calculations.

Suggestion:- Learn probability perfectly.

For more info watch movie:- The 21. which is a real story.

[XPAC03]

thank you

[jbenlez555]

whered you get subtracted from?

[Slade366]

Im in Algebra :D

[patrickJMT]

im in my house

[brittanyandjamie20]

tag

[brittanyandjamie20]

wtf

[joselosanchez]

In the back of the megamillions ticket says 1 between 175,000,000 the chances to win the jackpot, more simple...

[snitchboy12]

It's easy I won the Texas lotto 7 times.

[turmoildog]

suuuuuuuuuuuure u did...

[madhc44]

The Texas Lotto game actually has a much higher probability for winning, relatively speaking. In the Texas Lottery you select 6 from a field of 54. I think this is the multi-state Mega Millions game, though I suppose in Texas it is referred to as the Texas Millions.

I like your vids btw, very clear and concise explanations. Hard to find in a Calc II instructor!

[prettygangsta55]

Patrick will you do my math homework? Math 1314 at University of Houston lol.

[patrickJMT]

just drop it off in austin

[burby8100]

I always say the numbers that are not picked in awhile will show up like picking 1.

[Conceptzx2]

Great video. lol love your reference

[jetonm]

Hi Patrick,

I congratulate you about the vids you're showing. They are very helpful. I have a question though for another lottery scheme. The lottery has a total of 34 numbers of which 7 must be right to win the lottery. But you can pick 12 numbers (out of 34) from which only 7 must be the winning numbers. How do you find this probability?

[patrickJMT]

so you choose a total of 12, and of the seven that making the winning lotto number, you have to have those 7, correct?

[jetonm]

Correct! You choose a total of 12 out of 34. Of those 12, 7 ought to be correct to hit the winning number.

Thank you for your quick response.

[nkp777]

The way you describe is excellent,It's calculus made easy.

[patrickJMT]

i try to make my explanations as simply as possible... but not too simple!

[pitty031]

Great video Patrick. Please keep them coming..

[patrickJMT]

i will try!

[Waranle]

Thank you

[patrickJMT]

my pleasure waranle!

[magic100172]

guess not :( .. but meh.. have no plans to waste a dime on lotto in the near future =D

ps. especially after watching this vid !

[ardyay]

In paying taxes is also a waste of money.

[patrickJMT]

well, i dont know about that : )

i sort of like driving on paved roads, having public schools, having public parks, hospitals, firemen, policemen, public attorneys, etc., etc., etc. : ) However, as one can see from the US economic bailout plan, a lot of money gets wasted too unfortunately. now our tax dollars support people who make wooden arrows for children... what a waste! this is why all of u must study and change the world for the better! : )

or just suck it up and carry on!

[magic100172]

the probability of winning oz lotto is a little better ;D

[patrickJMT]

do ya get as much if u win though?! : )