A complex probability question

[issue]

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

 

[Mark44]

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.

The game with the return of the balls

What is the game?

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?

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.

 

[issue]

hey Mark44
Do you have a direction to solve the question?

 

[Office_Shredder]

I don't think we know what the question is. If you described the rules of the game they are not very clear.

 

[issue]

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?

 

[Mark44]

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.

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?

 

[issue]

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?

 

[Mark44]

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.

 

[Office_Shredder]

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?

 

[Mark44]

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.

 

[Office_Shredder]

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.

 

[issue]

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

 

[Mark44]

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).

Color red and then blue
0.389796213 X 0.433106904

 

[issue]

Geometric variable game calculation

 

[Mark44]

Geometric variable game calculation

?
No idea what this means.

 

[issue]

Builds something in Excel already sends

 

[issue]

Construction a simple way a formula that says (p * (1-p) ^ (game play-1)) * aximum value of previous game

what do you say ?

 

[issue]

 

[Mark44]

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.

 

[issue]

Anyway you can not get to big games. That's the point

 

[Office_Shredder]

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.

 

[issue]

I want to know what color ball came out in each game who plays number 1 until game 2324784

 

[Mark44]

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.