How to set up probability of numeric recurrence in lottery

In summary, the conversation is discussing how to set up a probability calculation for a lottery that draws 12 numbers from a hopper with values 0-9, where the probability of each number appearing remains constant. The person is looking for help in determining the probability of specific combinations of numbers appearing multiple times. The example used is rolling two dice and the chances of getting a specific number combination.
  • #1
ArfDogXYZ
1
0
Hi,
It has been a long time, and I do not remember how to set up a probability calculation with the following variables -
take a lottery that draws 12 numbers, values 0-9 only, from a hopper that replaces the number after it is drawn, i.e. probability of each number appearing remains constant.
How do I set up an equation to determine probability of, say
2 numbers each appearing 3 times
1 number 3 times and 1 number 4 times, etc... (can be any two numbers, just want to calculate probability of it happening at all, not for specific digits.)
any help appreciated, thanks
 
Physics news on Phys.org
  • #2
This is an easy problem. Take dice, what chance is there to get "snake eyes"? Well the 2 can occur in only one way (which is the case with the numbers you are mentioning) and so of the 36 possibilities with two dice there is only 1/36 chance that it will come on the next roll. To come up twice would be: 1/36 x 1/36 = 1/1296, but it will happen anyway!
 
  • #3


I would approach this problem by first understanding the basic principles of probability. In a lottery, the probability of a certain number being drawn is equal to the number of possible outcomes that include that number, divided by the total number of possible outcomes. In this case, there are 10 possible outcomes for each of the 12 numbers drawn, resulting in a total of 10^12 possible outcomes.

To determine the probability of 2 numbers each appearing 3 times, we can use the combination formula: nCr = n! / (r! * (n-r)!). In this case, n = 12 (total number of draws) and r = 3 (number of times the numbers appear). We can then calculate the probability for each of the 10 numbers and add them together to get the overall probability.

For the scenario of 1 number appearing 3 times and 1 number appearing 4 times, we can use a similar approach. We can first calculate the probability of one number appearing 3 times (using the same combination formula) and then multiply it by the probability of the other number appearing 4 times. Again, we can do this for all 10 possible number combinations and add them together to get the overall probability.

It is important to note that these calculations assume that the drawing process is truly random and that the probability of each number appearing remains constant. In reality, there may be other factors at play that could affect the outcome of the lottery. Additionally, these calculations only provide an estimate of the probability and cannot guarantee a certain outcome.
 

What is probability of numeric recurrence in lottery?

The probability of numeric recurrence in lottery refers to the likelihood that a set of numbers will be drawn in a specific order in a lottery game. This can be calculated by dividing the number of possible winning combinations by the total number of possible combinations.

How do I calculate the probability of numeric recurrence in lottery?

To calculate the probability of numeric recurrence in lottery, you need to determine the number of possible winning combinations and the total number of possible combinations. Then, divide the number of winning combinations by the total number of combinations to get the probability.

Can I improve my chances of winning by setting up the probability of numeric recurrence?

Setting up the probability of numeric recurrence in lottery does not guarantee a win, as lottery draws are based on chance. However, by calculating and understanding the probability, you can make informed decisions when choosing your numbers.

What factors influence the probability of numeric recurrence in lottery?

The probability of numeric recurrence in lottery can be influenced by the number of balls or numbers being drawn, the range of numbers to choose from, and the order in which the numbers are drawn. It can also vary depending on the specific rules and format of the lottery game.

Is there a way to increase the probability of numeric recurrence in lottery?

No, the probability of numeric recurrence in lottery cannot be increased. Each draw is independent and the chances of a specific set of numbers being drawn remain the same regardless of how many times they have been drawn in the past. The only way to increase your chances of winning is to purchase more tickets or to play more frequently.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
11
Views
1K
  • Precalculus Mathematics Homework Help
Replies
18
Views
276
  • Precalculus Mathematics Homework Help
Replies
23
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
25
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
768
  • Set Theory, Logic, Probability, Statistics
3
Replies
75
Views
6K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
837
Back
Top