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Questions tagged [lotteries]

Questions involving gaming games based on drawn numbers: Divisions, Systems and Dividends. Consider also using (combinatorics), (probability) or (betting) where appropriate.

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How much money would it cost to “buy out” every possible number in the 6-digit Lottery?

So, the constraints are as follows: First 5 numbers are digits 1 ; 69 The 6th number is a number 1 - 26 Order does not matter Numbers do not repeat Tickets cost $2 each My reasoning is as follows: ...
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29 views

Probability of Winning Fantasy 5 Lotto

In Fantasy 5, you choose 5 numbers, each 1-39. You win if you choose match all 5 numbers, but you can also win if you match 4, 3, or even 2 of the numbers. The lotto website lists the probabilities ...
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Weird lottery proabablity question

In this lottery $7$ balls are chosen from $1-60$. In order to win the main prize, you must select all $7$ right. I calculate the odds of doing this as: $$1:386,206,920$$ The odds of getting $3$ ...
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32 views

How do you create 10 discrete number combinations for a lottery?

In the lottery I participate in, the odds of winning the jackpot has been stated as being 1:5.4 million per row. Each coupon you hand in has 10 rows, where each row is a combination of 7 numbers out ...
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1answer
23 views

Probability lottery question with multiple variables to account for

Consider a state lottery where you get to choose 8 numbers from 1 to 80, no repetition allowed. The Lottery Commission chooses 11 from those 80 numbers, again no repetition. You win the lottery if at ...
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60 views

Why exactly “(1-p) math” gives wrong probability of next lottery draw if something special happened many times in a row (10 even => play odd)?

Let's take not odds/even example, but a more complicated one, but same logic can be applied to both. Given some lottery, say $5$ out of $36$ lottery ($5$ unique numbers out of pool of $36$ numbers ...
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Math probability that “5-out-of-36” lottery draw has at least one pair of numbers with difference = 1.

Given a $5$ out of $36$ lottery ($5$ unique numbers out of pool of $36$ numbers ranging $[1,2,…,36]$). How to calculate probability that a draw has at least one pair of consecutive numbers (like ...
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1answer
44 views

Probability of not guessing any number in lotto drawing 7/34

I'm trying to calculate the probability of not guessing any numbers in a 7/34 lotto drawing. My approach was to multiply the probabilities of guessing a single number 7 times in a row while removing 1 ...
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Mega millions: how likely is it to be this close?

Someone sent this around at the office, as a unique show of how unlucky one can be: First, spit-balling in my head, I replied "oh, that's not that unlikely, there must be hundreds or thousands of ...
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808 views

Calculate lottery's second prize using combination - lottery probability question.

Assume a lottery game of the following rules: Picking your numbers: Pick a total of 6 different numbers from the lot containing 42 numbers (1 to 42). Draw: Draw 7 balls, with no repetition(i.e: ...
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Probability of winning the lottery: how are those two interpretations different?

Winning this specific lottery consists of choosing 5 numbers from a list of 50 numbers $\{1,2,3,...,50\}$ and then choosing 2 numbers from a list of 9 $\{1,2,...,9\}$. You win if all your numbers are ...
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Boxed lottery tickets, rencontres numbers and number of degree-$n$ permutations of order exactly $d$

This is a question that I encountered at work that I am trying to get a deeper understanding of. We sell tickets in a lottery where you guess $4$ numbers out of range of $36$ (the range is irrelevant ...
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2answers
39 views

Lottery ticket sales and ‘coverage’

Take a small 6/40 lottery with 3,838,380 possible combinations. Prior to the draw, the operator sells only 3 million randomly drawn tickets (for simplicity’s sake, I’m completely ignoring the fact ...
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1answer
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Probability of winning with multiple tickets in multiple draws

Unfortunately, after hours of searching I was unable to find an answer to the following scenario: Let's assume I play five unique combinations in a weekly 6/49 lottery, where the chance of matching ...
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595 views

UK Lottery Odds Calculation Error

I found the probability topic in stats and mechanics to be very interesting, and I attempted to try using it to calculate the odds of winning the UK National Lottery, but failed. My calculation was (1/...
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37 views

Are the two item selection turn lottery methods identical?

Owners of a land plot build a building together, in which there are many apartments. Every owner has the right to own a certain number of apartments. The sum of the rights of all owners is equal to ...
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1answer
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Calculating permutations when an event can end the game

There are 50 balls. 40 Black and 10 White. You draw balls without replacement and win if you draw all 10 white balls before drawing 4 black balls in a row. How do I calculate the probability of ...
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Probability: independant lottery ticket

I have one chance over 1,000,000 to win a lottery. If I buy the same number of ticket with different combination on each, I have 100% chance of winning. What if my ticket number are randomly choosen ? ...
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3answers
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How many powerball tickets will guarantee a 3/5 match?

Trying it figure this out, but looks like the obvious answer might not be right. According to the probabilities there is a 1 in 579.76 chance of matching 3 of 5 numbers in a Powerball ticket. So how ...
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3answers
62 views

What is best strategy in a slightly biased lottery with known differences of frequency of some balls?

I know for sure which numbers appear more often in a 5 out of 36 lottery (5 unique numbers out of pool of 36 numbers ranging [1,2,…,36]). I know that 4 balls appear more often than the average, 11 ...
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2answers
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Lottery - better try to hit numbers-group that appears often, than hope for a “one-in-thousand-years” combination? [duplicate]

Please correct my reasoning: There is a 5 out of 36 lottery (5 unique numbers out of pool of 36 numbers ranging [1,2,…,36]). Strategy 1: just play any random combination. Like 12345, or better 11111....
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Play 100 tickets in one lottery draw or 100 plays/draws with 1 ticket - same chances to win?

5/49 lottery is when 5 different numbers are selected (without replacement) out of 49 possible numbers in range 1..49. Total number of possible combinations is C(49, 5). (1) If I make a stake once ...
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1answer
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Better play 100 tickets in one lottery draw or 100 plays/draws with 1 ticket?

I heard many people say that it is better to play 100 tickets in one draw of 5/49 lottery, rather than 100 plays/draws with 1 ticket. Is there any scientific basis for this, or actually there is no ...
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381 views

What probability distribution is best to describe lotteries?

What kind of probability distribution is best suited to describe lotteries? Wikipedia provides extensive list of probability distributions (another list of them - see at bottom). But reading ...
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powerball draw question

This seems intuitive but would like a second opinion. Powerball with 69 numbers. Need to choose 5 correct (order does not matter). ...
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1answer
42 views

Probability for a lottery [closed]

What's probability to choose the 6 correct numbers in a lottery (made up of 42 numbers)? I do know how to do it with combinatorics $${42 \choose 6} = (42·41·40·39·38·37)\div ( 1·2·3·4·5·6) = ...
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1answer
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Defining a probability of success in a lottery

Suppose that I have the following lottery: $p(x)W-(1-p(x))L$ Where $p$ is the probability of winning W and x is a variable that influences the probability of success. The expected utility for the ...
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2answers
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Probability of getting 7 numbers smaller or equal to 59, from a draw of 20 numbers out of 80

What is the Probability of getting $7$ numbers smaller or equal to $59$, from a draw of $20$ numbers out of $80$? I can work out the probability of getting them in the 1st $7$ numbers $$59/80 * 58/...
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Maximum Likelihood Estimator of number of lottery tickets

A lottery has $N$ tickets numbered $1, 2, \dots, N$ with $N$ unknown. A random sampling of 5 winning tickets is numbered, say, $\{a, b, c, d, e\}\in[1, N]$. The question I am trying to solve gives $...
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3answers
242 views

Probability of binomial distribution with dependent events

Problem: I played lottery and I bought $5000$ numbers of $100.000$. In the raffle, there are $2000$ prizes (or $2000$ tests), in that $2000$ prizes, $5$ are high prizes. Question: What's my ...
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1answer
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Probability of finding a random number in a random interval vs. random samples

Suppose there is a lottery where a random natural number between 1 and n = 1000 is drawn in secret. They sell two different tickets to customers: A ticket with k = 10 random numbers on it (not sorted,...
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Which route is better for a Neutral-risk person?

There are two routes, 1 and 2. It is known that route 1 takes 60 minutes and route 2 takes 41 minutes. If there is problems in the traffic: Route 1 will increase to 70 minutes; Route 2 will ...
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78 views

Euromillions - Does covering all the balls across a number of tickets increase chances of a (small or large) win?

So in the UK the Euromillions lottery tonight will be £167M. For those outside Europe, a Euromillions ticket consists of 5 numbers (from 1-50) and 2 lucky stars (from 1-12). Jackpot is won if the ...
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Long term lottery probability with multiple-number tip

There is a lottery where is drawn six numbers out of 49 with two draws per day. In this lottery is possible to select in one ticket more than six numbers - i.e. when you select 8 numbers then your ...
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2answers
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Probability of two people winning a prize, according to the number of tickets each person has

Since I find it hard to abstractly describe what I want to understand, I came up with the following example. Suppose that 6 people hold each a given number of a very special type of lottery tickets. ...
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how do you calculate gold lotto

For my assignment I am trying to calculate the probabilities of Australian Saturday gold lotto (45 balls 6 winning 2 supplementary). I need help finding the division calculations to find the division ...
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226 views

Consecutive subset in lottery

What is the probability that in 7 drawn numbers in lottery (out of 39) there are 4 consecutives? I have been chasing my tail here. So, we have $39-3=36$ sequences of 4 consecutive numbers. If we ...
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lotto advice debunking [closed]

In lotto game 7/39, combination of 7 numbers are drawn at random. Should we trust 'lotto experts' and their lotto advice? For example, should we pick 4 of the higher and 3 out of the lower numbers (...
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3answers
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Probability that the second and third card extracted are both aces?

I would like to know if the following reasoning is correct: the situation is the extraction without replacement of 3 cards out of 40, where there are 4 aces. I would say the cardinality of the sample ...
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2answers
117 views

Probability that at least two equal numbers are extracted

Consider an urn containing 90 balls numbered from 1 to 90, plus 3 balls attached with 3 distinct (known) numbers still from 1 to 90, say 1,2,3. I'm trying to find the probability that at least two ...
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355 views

What is the expected value of a lottery ticket if one could wait finitely many draws to try to get the highest prize?

Normally, lottery tickets are valid for only one drawing. If one wants to play the same numbers for multiple draws, the cost of the ticket is multiplied accordingly. What if one could hold on to it ...
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How did Mohan Srivastava crack Ontario scratchcards?

Wired ran a 2011 article about how a statistician, Mohan Srivastava, cracked Ontario scratchcards such as this one. First, he thought about the program that produced the numbers on the cards. 'Of ...
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3answers
642 views

Lottery probability, picking 10 numbers to get 6 winning numbers

What are your chances of winning in the following scenario? Consider a lottery game with 49 numbers and 6 are chosen as the winning numbers. You're allowed to select 10. What is the probability that ...
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Predicting lottery numbers

I am working on a model and formula for predicting lotto numbers. Some success. Looking at recent ozlotto and sat lotto draws (pics). There were a total of 19 numbers drawn (2x sat (6 numbers)) and 1x ...
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In a country's State Lottery, five balls are drawn (without replacement) from a drum filled with balls numbered from 1 to 45.

When buying a ticket an entrant chooses five numbers between 1 and 45 inclusive. To win a prize in a lottery, at least three of the balls drawn must match numbers on one's ticket. To win the jackpot, ...
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Combinations and the EuroMillions lottery even when another Lucky Star is added.

Firstly my level of mathematics understanding is only at O level or GCSE level if you like however my education level is just under degree level having a HND in Computer Science. Someone is saying ...
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307 views

On the EuroMillions lottery

To play the EuroMillions lottery, one selects five main numbers from $1$ to $50$ and two Lucky Stars numbered from $1$ to $11$. I would like to know what the number of possibilities is given the ...
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1answer
168 views

Determine if this lottery system is profitable

I have a problem where I'm supposed to determine if a lottery system is profitable. I solved the problem and found it to be profitable, but I am not 100% sure about all of my calculations. Below is ...
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1answer
258 views

Probability of winning the jackpot at a certain state's lottery [closed]

A certain state's lottery consists of choosing $6$ numbers at random without replacement from the set $\{1,2,3,\ldots,40\}$. What is the probability that someone wins the jackpot? I just want to ...
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What is the probability that the number “3” gets picked up at EuroMillions?

EuroMillions is a game where you have to tick 5 numbers in a grid of 50 numbers (from 1 to 50) (there is also a stars system, but let's omit it). Then, the draw: 50 balls numbered from 1 to 50 in box, ...