A complex probability question

In summary: I added a bit more to my reply right after you posted. If the balls aren't replaced after being selected, it has to affect the probabilities. For example, suppose we looked in the pitcher and selected pink balls for the first 50,000 trials. If we reach in without looking for the 50,001st trial, the probability of getting a pink...
  • #1
issue
15
0
Homework Statement
probability question
Relevant Equations
Binomial distribution
There is a box with 2324784 bullets. Balls are divided into 5 groop and there is a definition for each groop and how many balls and what is the probability of getting each groop. The game with the return of the balls

List the probability and quantity

groop 1 906192 0.389796213
groop 2 1006880 0.433106904
groop 3 143840 0.061872415
groop 7 215760 0.092808622
groop 8 52112 0.022415846

Question: Is it possible to calculate the best groop probability for any amount of games- 2324784 games

Actions I performed and i failed

Making a probability tree impossible
1- The tree grows mediocre 5 options 25 options 125 options and so on

2. Binomial distribution - After 500 can not be calculated

3. Ramsey theory - very complex

If there is anyone sharp here I would love to hear a new theory

Thank you to all respondents
 
Physics news on Phys.org
  • #2
issue said:
Homework Statement:: probability question
Relevant Equations:: Binomial distribution

There is a box with 2324784 bullets. Balls are divided into 5 groop and there is a definition for each groop and how many balls and what is the probability of getting each groop.
Bullets or balls? It doesn't really matter, but it's nice to be consistent.
issue said:
The game with the return of the balls
What is the game?
issue said:
List the probability and quantity

groop 1 906192 0.389796213
groop 2 1006880 0.433106904
groop 3 143840 0.061872415
groop 7 215760 0.092808622
groop 8 52112 0.022415846

Question: Is it possible to calculate the best groop probability for any amount of games- 2324784 games
Again, what constitutes a game?
issue said:
Actions I performed and i failed

Making a probability tree impossible
1- The tree grows mediocre 5 options 25 options 125 options and so on

2. Binomial distribution - After 500 can not be calculated
Multinomial probability based on the fact that there are five groups.
 
  • #3
hey Mark44
Do you have a direction to solve the question?
 
  • #4
I don't think we know what the question is. If you described the rules of the game they are not very clear.
 
  • #5
Mark44 said:
Bullets or balls? It doesn't really matter, but it's nice to be consistent.
What is the game?
Again, what constitutes a game?
Multinomial probability based on the fact that there are five groups.
here is a pitcher with 2324784 balls.

Number of balls in red color 906192 Probability in game 0.389796213
Amount of balls in blue color 1006880 Probability in game 0.433106904
Amount of balls in yellow color 143840 Probability in game 0.061872415
Amount of balls in 215760 Probability per game 0.092808622
The amount of balls in pink 52112 probability in the game 0.022415846

Games 2324784 Games. In each round, the ball that is returned is returned. Is it possible to calculate the ball that came out for each round for 2324784 games?
 
  • #6
issue said:
here is a pitcher with 2324784 balls.

Number of balls in red color 906192 Probability in game 0.389796213
Amount of balls in blue color 1006880 Probability in game 0.433106904
Amount of balls in yellow color 143840 Probability in game 0.061872415
Amount of balls in 215760 Probability per game 0.092808622
The amount of balls in pink 52112 probability in the game 0.022415846

Games 2324784 Games. In each round, the ball that is returned is returned.
In each trial, someone picks a ball out of the pitcher/basket/whatever.
After the ball is selected, is it replaced in the pitcher? It makes a difference whether each ball is replaced or not after it is selected.
issue said:
Is it possible to calculate the ball that came out for each round for 2324784 games?
No. All you can do is calculate the probability of each color ball being chosen.

Is there some significance in working with 2,324,784 balls?
 
  • #7
Mark44 said:
In each trial, someone picks a ball out of the pitcher/basket/whatever.
After the ball is selected, is it replaced in the pitcher? It makes a difference whether each ball is replaced or not after it is selected.

No. All you can do is calculate the probability of each color ball being chosen.

Is there some significance in working with 2,324,784 balls?
Is there some significance in working with 2,324,784 balls?NO . How can I calculate the probability of game number 500 which ball came out?
 
  • #8
issue said:
How can I calculate the probability of game number 500 which ball came out?
Are the balls replaced in the pitcher after each trial? It makes a difference whether they're being replaced or not. If they're being replaced after each trial, then the probability of picking a given ball is the same on the first trial or the 500th trial.
 
  • #9
Mark44 said:
Are the balls replaced in the pitcher after each trial? It makes a difference whether they're being replaced or not.
If you're just asking about the color of ball 500, I think it doesn't actually?
 
  • #10
Office_Shredder said:
If you're just asking about the color of ball 500, I think it doesn't actually?
I added a bit more to my reply right after you posted. If the balls aren't replaced after being selected, it has to affect the probabilities. For example, suppose we looked in the pitcher and selected pink balls for the first 50,000 trials. If we reach in without looking for the 50,001st trial, the probability of getting a pink ball is much lower than the original probability.
 
  • #11
Sure, but if the question is just 'what is the probability ball 500 is pink with no other information" then it's just the fraction of balls that are pink at the start.
 
  • #12
This is a true theory. But not accurate
It's like a probability tree each round multiplies a previous branch
The chance of getting a red color in round 2 is
0.389796213 X 0.389796213 =
Color red and then blue
0.389796213 X 0.433106904
If you want to know what came out in round 5000 you have to do all the way who round 1 maybe I'm
 
  • #13
issue said:
This is a true theory. But not accurate
It's like a probability tree each round multiplies a previous branch
The chance of getting a red color in round 2 is
0.389796213 X 0.389796213 =
No. What you're describing is the probability of getting a red ball in the first trial and then another red ball in the second trial. For any given trial, P(red ball) = .389796213 (assuming replacement).
issue said:
Color red and then blue
0.389796213 X 0.433106904
 
  • #14
Geometric variable game calculation
 
  • #15
issue said:
Geometric variable game calculation
?
No idea what this means.
 
  • #16
Builds something in Excel already sends
 
  • #17
Construction a simple way a formula that says (p * (1-p) ^ (game play-1)) * aximum value of previous game

what do you say ?
 

Attachments

  • test1.xlsx
    53.3 KB · Views: 102
  • #18
 
  • #19
issue said:
Builds something in Excel already sends
Reading from right to left, each row in your Excel spreadsheet represents the probabilities of picking 1, 2 ,3 ... balls of the same color.
 
  • #20
Anyway you can not get to big games. That's the point
 
  • #21
I still don't understand exactly what you want to compute, but a lot of what is being talked about in this thread is ready to calculate.
 
  • #22
I want to know what color ball came out in each game who plays number 1 until game 2324784
 
  • #23
issue said:
I want to know what color ball came out in each game who plays number 1 until game 2324784
Probability doesn't work that way. All it can tell you is whether it's more likely or less likely a particular color gets chosen. It cannot tell you which ball gets selected on each trial.

Since your question has been answered, I am closing this thread.
 
  • Like
Likes SammyS and issue

1. What is a complex probability question?

A complex probability question is a mathematical problem that involves multiple variables and conditions, making it difficult to solve using basic probability principles. It often requires advanced mathematical techniques and critical thinking skills to arrive at a solution.

2. How do you approach a complex probability question?

The first step in approaching a complex probability question is to carefully read and understand the problem. Then, identify the given information and the variables involved. Next, use the appropriate probability formulas and techniques to solve the problem. It may also be helpful to break the problem down into smaller, more manageable parts.

3. What are some common techniques for solving complex probability questions?

Some common techniques for solving complex probability questions include using tree diagrams, Venn diagrams, and the multiplication and addition rules of probability. Other techniques may include using conditional probability, Bayes' theorem, and combinatorics.

4. How can I check my answer to a complex probability question?

To check your answer to a complex probability question, you can use a calculator or a spreadsheet to perform the necessary calculations. You can also double-check your work by using alternative methods or by working backwards from the given answer to see if it satisfies all the conditions of the problem.

5. How can I improve my skills in solving complex probability questions?

To improve your skills in solving complex probability questions, it is important to practice regularly and familiarize yourself with different types of problems. You can also seek help from textbooks, online resources, or a tutor to learn new techniques and strategies. It is also helpful to break down problems into simpler parts and to carefully analyze each step of the solution process.

Similar threads

  • Set Theory, Logic, Probability, Statistics
2
Replies
41
Views
3K
  • Math Proof Training and Practice
3
Replies
82
Views
11K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
2K
Replies
9
Views
47K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
20
Views
4K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
7
Views
2K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
9
Views
2K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
8
Views
3K
Back
Top