# A Question About Probabilities (Lottery Related) **URL:** \ **Category:** Factual Questions\ **Created:** [August 25, 2011, 11:01pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096 "2011-08-25T23:01:11Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Mean\_Mr.Mustard](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mean_mr.mustard/32/3865_2.png) [@Mean\_Mr.Mustard](https://boards.straightdope.com/u/Mean_Mr.Mustard)\ **Post date:** [August 25, 2011, 11:01pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/1 "2011-08-25T23:01:11Z")
The odds of winning the PowerBall jackpot are 1 in 195,249,054. This means that the odds of winning if I buy \*two \*tickets are 1 in 97,624,527, yes? Assuming this is true, what is the calculation to determine my odds if I buy, say, 25 tickets? Thanks, mmm ---
**Author:** ![Rekd](https://avatars.discourse-cdn.com/v4/letter/r/5f8ce5/32.png) [@Rekd](https://boards.straightdope.com/u/Rekd)\ **Post date:** [August 25, 2011, 11:06pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/2 "2011-08-25T23:06:33Z")
195,249,054 / 25? I hope you know that the Lottery is simply a tax for people that are bad at math. Take a trip to a horse-shoe pit and look at the sand. Now consider the probability of picking up a certain 25 grains of sand. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 25, 2011, 11:06pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/3 "2011-08-25T23:06:37Z")
Assuming that you make sure to pick different numbers on all of them, just divide 195,249,054 by 25. ---
**Author:** ![Lare](https://avatars.discourse-cdn.com/v4/letter/l/53a042/32.png) [@Lare](https://boards.straightdope.com/u/Lare)\ **Post date:** [August 25, 2011, 11:07pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/4 "2011-08-25T23:07:56Z")
I believe it’s 25 in 195,249,054, which, if I had a calculator I could state in terms of “one in…” ---
**Author:** ![zombywoof](https://avatars.discourse-cdn.com/v4/letter/z/9e8a1a/32.png) [@zombywoof](https://boards.straightdope.com/u/zombywoof)\ **Post date:** [August 25, 2011, 11:15pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/5 "2011-08-25T23:15:01Z")
> [@Lare](#): > > if I had a calculator Just Google 195,249,054/25 - it’s a calculator. ---
**Author:** ![robert\_columbia](https://avatars.discourse-cdn.com/v4/letter/r/e79b87/32.png) [@robert\_columbia](https://boards.straightdope.com/u/robert_columbia)\ **Post date:** [August 25, 2011, 11:54pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/6 "2011-08-25T23:54:05Z")
25/195,249,054, I believe. There are 195,249,054 possible outcomes, and 25 of them would work to your advantage. The second ticket doubles your changes. To double your chances again, you need to double the number of tickets you have, not just buy another. ---
**Author:** ![Mean\_Mr.Mustard](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mean_mr.mustard/32/3865_2.png) [@Mean\_Mr.Mustard](https://boards.straightdope.com/u/Mean_Mr.Mustard)\ **Post date:** [August 26, 2011, 12:00am UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/7 "2011-08-26T00:00:32Z")
As usual, I was over thinking the thing. Thanks, all. mmm ---
**Author:** ![mac\_bolan00](https://avatars.discourse-cdn.com/v4/letter/m/b3f665/32.png) [@mac\_bolan00](https://boards.straightdope.com/u/mac_bolan00)\ **Post date:** [August 26, 2011, 12:27am UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/8 "2011-08-26T00:27:44Z")
if it’s the ping pong ball format wherein you draw 6 balls, each with a number from 0 to 100, it’s 101 raised to the sixth or 1.06 billion per ticket. ---
**Author:** ![Lare](https://avatars.discourse-cdn.com/v4/letter/l/53a042/32.png) [@Lare](https://boards.straightdope.com/u/Lare)\ **Post date:** [August 26, 2011, 3:06pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/9 "2011-08-26T15:06:54Z")
> [@zombywoof](#): > > Just Google 195,249,054/25 - it’s a calculator. :smack: Is there nothing The Google can’t do? ---
**Author:** ![JohnT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnt/32/15048_2.png) [@JohnT](https://boards.straightdope.com/u/JohnT)\ **Post date:** [August 26, 2011, 4:36pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/10 "2011-08-26T16:36:23Z")
Clean my house. :mad: ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 26, 2011, 5:43pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/11 "2011-08-26T17:43:39Z")
> [@Rekd](#): > > 195,249,054 / 25? I hope you know that the Lottery is simply a tax for people that are bad at math. What if you’re good at math, but happen to prefer the high probability of a small monetary loss/low probability of a large monetary win to the guarantee of staying the same? Is insurance also a tax for people who are bad at math? ---
**Author:** ![obfusciatrist](https://avatars.discourse-cdn.com/v4/letter/o/4af34b/32.png) [@obfusciatrist](https://boards.straightdope.com/u/obfusciatrist)\ **Post date:** [August 26, 2011, 5:53pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/12 "2011-08-26T17:53:14Z")
> [@Indistinguishable](#): > > Is insurance also a tax for people who are bad at math? Depends on how much you pay for the insurance and the risk you’re insuring against. ---
**Author:** ![Lukeinva](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lukeinva/32/17872_2.png) [@Lukeinva](https://boards.straightdope.com/u/Lukeinva)\ **Post date:** [August 26, 2011, 5:56pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/13 "2011-08-26T17:56:00Z")
> [@zombywoof](#): > > Just Google 195,249,054/25 - it’s a calculator. The answer is: 7 809 962.16 Still not too good. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [August 26, 2011, 7:17pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/14 "2011-08-26T19:17:17Z")
> [@Indistinguishable](#): > > What if you’re good at math, but happen to prefer the high probability of a small monetary loss/low probability of a large monetary win to the guarantee of staying the same? > > Is insurance also a tax for people who are bad at math? It’s a question of expected utility. In general the more money you have the less the utility of that money. Ten bucks means more to a poor person than to a rich person. So if you have $100,000, winning another $100,000 is less than 1,000 times as useful as saving $100.00 However with insurance, spending $100 on insurance is less than 1,000 times as bad as dropping from $100,000 to zero. Also, insurance gives you better odds than the lottery. That said, my wife sometimes buys lottery tickets saying she gets more than $1 worth of hopes and dreams out of them, and who am I to argue that. ---
**Author:** ![FlippyFly](https://avatars.discourse-cdn.com/v4/letter/f/e95f7d/32.png) [@FlippyFly](https://boards.straightdope.com/u/FlippyFly)\ **Post date:** [August 26, 2011, 7:19pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/15 "2011-08-26T19:19:41Z")
I don’t think this is right… take the example of a coin toss. You have a 1 in 2 chance of flipping heads, but that doesn’t mean if you flip it twice you will get heads. I believe the correct way to calculate the odds is to take the odds of losing (195,249,053 out of 195,249,054) and multiple that times itself 25 times, then subtrace the answer from 1 to get your odds of winning. In the penny example, flipping once gives you a 50% chance of a ‘win’ with heads. Flipping twice gives you a 25% chance of tails both times (1/2 x 1/2 = 1/4) and subtracting this from one gives you a 75% chance of a ‘win’ with heads on at least one flip. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [August 26, 2011, 9:02pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/16 "2011-08-26T21:02:29Z")
> [@FlippyFly](#): > > I don’t think this is right… take the example of a coin toss. You have a 1 in 2 chance of flipping heads, but that doesn’t mean if you flip it twice you will get heads. > > I believe the correct way to calculate the odds is to take the odds of losing (195,249,053 out of 195,249,054) and multiple that times itself 25 times, then subtrace the answer from 1 to get your odds of winning. > > In the penny example, flipping once gives you a 50% chance of a ‘win’ with heads. Flipping twice gives you a 25% chance of tails both times (1/2 x 1/2 = 1/4) and subtracting this from one gives you a 75% chance of a ‘win’ with heads on at least one flip. One of the earlier posters made the assumption that all of the lottery tickets showed a different number so this reasoning was not in play. That would be a sensible strategy for picking tickets since there is no point in dividing the prize with yourself. If the tickets are chosen at random so that duplicates are possible then you are technically correct. This follows from the fact that in multiple tries it is possible to win more than once, but still only count as a single tiome for determining wehter you won or not. However, given that the probability of winning once in 25 tickets is very small, the probability of winning twice is so absolutely miniscule that it won’t really affect things. I calculate that it reduces your chances from 1 in 7,809,962.16 to 1 in 7,809,962.58 ---
**Author:** ![Alley\_Dweller](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alley_dweller/32/430_2.png) [@Alley\_Dweller](https://boards.straightdope.com/u/Alley_Dweller)\ **Post date:** [August 26, 2011, 9:22pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/17 "2011-08-26T21:22:23Z")
> [@FlippyFly](#): > > I don’t think this is right… take the example of a coin toss. You have a 1 in 2 chance of flipping heads, but that doesn’t mean if you flip it twice you will get heads. > > I believe the correct way to calculate the odds is to take the odds of losing (195,249,053 out of 195,249,054) and multiple that times itself 25 times, then subtrace the answer from 1 to get your odds of winning. > > In the penny example, flipping once gives you a 50% chance of a ‘win’ with heads. Flipping twice gives you a 25% chance of tails both times (1/2 x 1/2 = 1/4) and subtracting this from one gives you a 75% chance of a ‘win’ with heads on at least one flip. Assuming you can choose your own lottery numbers and don’t choose the same numbers twice, this is a better analogy for the lottery question: A coin flip is scheduled for 7:00 p.m. on Friday. If you place a bet on heads, you have a 50% chance of winning the flip. If you also place a second bet on on tails, between the two bets, you have a 100% chance of winning when they flip the coin. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 26, 2011, 9:25pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/18 "2011-08-26T21:25:18Z")
> [@Buck\_Godot](#): > > It’s a question of expected utility. Expected utility/loss is not really a good way of dealing with insurance risks for the simple reason that there’s a really big difference between your expected loss due to certain rare events and your expected loss due to these events conditional on that loss being nonzero. I’ve never seen an actuarial analysis of the powerball, but I can’t imagine that it’d be as simple as taking the choice with the higher expected utility. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 26, 2011, 11:17pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/19 "2011-08-26T23:17:45Z")
> [@Buck\_Godot](#): > > It’s a question of expected utility. If you like. But even on that analysis, a person may perfectly reasonably have such a utility function as that the expected utility of playing the lottery is positive. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 26, 2011, 11:23pm UTC](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096/20 "2011-08-26T23:23:13Z")
(That is, the marginal utility of a dollar needn’t _always_ decrease with income) [Next page](https://boards.straightdope.com/t/a-question-about-probabilities-lottery-related/594096.md?page=2)