Lottery System
The lottery system is an entertainment strategy of playing the lotteries widely used by individuals players and syndicates to secure wins provided they hit some of the drawn numbers. Lottery systems allow members to play with one or more than one ticket and more numbers than those drawn in the lottery. if the lottery picks 5, then the lottery system can be used in playing with 6 or more than 6 members. If the lottery picks 6 then the lottery system can be used in playing with 7 or more than 7 members.
For example, if the lottery picks 5, then the lottery system can have 9 members and assurance of 3 if 3, meaning the player will get a 3 win whenever three of his/her 9 numbers are drawn among the 5 numbers drawn. Similarly, if the lottery is picked 6, then the lottery system can have 12 members and assurance of 4 if 5, meaning the player will get a 4 win whenever five of his/her 12 numbers are drawn among the 6 numbers drawn.
A lottery system acts as a single ticket in terms of a particular assurance, but it allows playing with a set of a number size larger than the size of the set of numbers drawn in a lottery. Lottery systems enable players to play with as many numbers as they wish in a well-structured way.
What is Lottery?
A lottery is a sort of gambling where people buy tickets and win if his/her number is chosen. It is a game of chance in which winning players are selected randomly. Lotteries can be used in decision-making tasks such as sports team drafts and the distribution of scarce medical treatment.
Lottery Meaning In Mathematics
In Mathematics, the lottery is used to calculate the probabilities of winning or losing a game. Lottery is highly based on combinatorics, specifically the twelvefold way and combinations without substitutions.
Lottery Formulas
Different lotteries have different lottery formulas.
Here we will discuss a typical lottery where players will select 6 different numbers out of 49.
In a 6/49 game, a player will choose 6 different numbers from a range of 1- 49.
You choose numbers: 1,12,14, 20, and 21.
On Sunday, the players drew the lottery and the winning numbers were 3,12,18, 20, 32, and 43.
Your two of the numbers are matched ( 12 and 20).
Is matching 2 numbers enough to win something ( No).
You should match at least 3 number to receive a small prize.
Matching 4 numbers gets a bigger prize.
Matching 5 numbers get even a bigger prize.
You might win in millions if all the 6 numbers are matched.
The probability of winning all 6 numbers is 1 in 13, 983,816.
The probability of winning all 6 numbers in 6/49 games can be calculated by using the following lottery formula:
\[\binom{n}{k} = \frac{n!}{k!(n-k)!}\]
Here, n is the number of different alternatives and k is the number of choices.
\[\binom{n}{k} = \frac{49!}{6!(49 - 6)!}\]
= \[\frac{49 \times 48 \times 47 \times 46 \times 45 \times 44}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 13, 983,816\]
So how many times should you play to win the big prize?
One Week
Suppose you play every week. The probability of winning after 1 week is:
\[\frac{1}{13,983,816} = 0.0000000715\]
The probability of no winning after 1 week is \[1 - \frac{1}{13,983,816} = 0.9999999285\]
50 Years
Suppose you play for 50 year that is 2600 weeks.
The probability of no winning over 2600 week is \[(1- \frac{1}{13,983,816})^{2600} = 0.999814\]
The probability of winning over 2600 week or 50 years is 1 - 0.999814 = 0.000186…
Solved Example
1. Find the odds of winning the lottery if 5 tickets are purchased out of the total 50 lottery tickets sold and the total ticket sold will be the winner is 20.
Solution:
Given,
Ticket sold = 5
Winners = 20
Tickets Purchased = 5
Here, the odds of winning the lottery can be calculated using the following lottery formula:
\[(1 - (1 - \frac{W}{T})\]
Here,
T - Total number of tickets that will be sold.
W - Total number of tickets that will be winner.
P - Total number of tickets that will be purchased.
Substituting the values in the above lottery formula, we get,
\[(1 - (1 - \frac{20}{50})^{5} \times 100\]
= 92.22%
Fun Facts
1 in the 5 top game prizes in the UK across EuroMillions, Lotto and EuroMillions UK Millionaire Maker are won by syndicates.
FAQs on Lottery
1. How the Odds of Winning the Lottery can be Calculated?
Ans: To calculate the odds of winning the lottery, first, we need to determine the number of combinations. We use the binomial coefficient formula to determine the total possible combination. The following binomial coefficient formula can be used to calculate the odds of lottery winnings.
(nk) = n!/[k!(n - k)!\]
Here, n is the size of the number field, and k is the pick size.
Hence, in a lotto 6/49 system, n = 49 and k = 6.
2. What Should be the Minimum Number of Tickets to be Purchased for a Match?
Ans: It is often problematic to calculate the minimum number of tickets one needs to purchase to assure that at least one of these tickets matches at least 2 numbers. In the 5/90 lotto system, the minimum number of tickets that can guarantee a ticket with a minimum of 2 matches is 100.
3. What is the Lottery Syndicate?
Ans: A lottery syndicate is a group of people who plays the lottery together. By pulling the syndicate's money and purchasing multiple tickets collectively, players increase the chance of winning the lottery draw and share any winnings among them.
