# Play the Probability Game: Test Your Luck!

• Shackleford
In summary: So your probability of winning in 4 throws is 1/4.Wow, you evaded any meaningful answer again. Yes, your probability of getting any given number is 1/4. Now tell me something about how that would translate into a probability of winning the game at any given n. Any n, you pick.That's not how probability works. Probability is not a number. It's a concept.
Well, firstly

P(win| R_0 = 1) = P(win| R_0 = 2) = P(win| R_0 = 3) = P(win| R_0 = 4).

So you just need to find anyone of them and that's your probability.

Now do it for special cases -

1. What is the probability that he wins in 1 try?
2. 2 tries?
3. 3 tries?
4. 4 ... ?

Do you see a pattern?

The answer is then the infinite sum

P(win) = $\sum_{n=1}^{\infty}$P(win in n tries)

Well, I suspected some sort of pattern last night. If you break up one of those tries into "equals 1" and "not equals 1," the "not equals 1" will translate into R2=R1, R2=R0, and again R2 not = R1.

Well, so did you work it out? Kindly post what you have been able to do.

praharmitra said:
Well, so did you work it out? Kindly post what you have been able to do.

I just got home.

Oh, I'm supposed to work out when you win in a certain number of tries. Let me do that in a few minutes.

Shackleford said:
I just got home.

Oh, I'm supposed to work out when you win in a certain number of tries. Let me do that in a few minutes.

This problem is actually fairly tricky unless you are used to Markov chain sorts of problems. It branches depending on whether you win or continue at stages. Took me a few false tries to get it right. But praharmitra is correct. Doing some special cases of n will really help to see the general pattern.

I have heard of Markov chains, but I have no idea what they are nor have I encountered them in coursework.

This is probably not correct.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110409_224337.jpg?t=1302407152

Last edited by a moderator:
Shackleford said:
I have heard of Markov chains, but I have no idea what they are nor have I encountered them in coursework.

This is probably not correct.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110409_224337.jpg?t=1302407152

Ok, so what is that blurry thing you posted supposed to tell me? What is the probability of winning at say n=1, n=2, n=3 and n=4? Solving the whole question may be a little subtle, but those special cases are easy. Do them. Do something.

Last edited by a moderator:
Shackleford said:
I have heard of Markov chains, but I have no idea what they are nor have I encountered them in coursework.

This is probably not correct.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110409_224337.jpg?t=1302407152

It's not only not correct. It has no content whatsoever. Give us some numbers. A Markov chain is a sequence of events where you have a potentially infinitely recurring state. This is one. There may be a more elementary way to solve this but I haven't thought of it. Maybe it you just write out enough special cases of n you can see the pattern.

Last edited by a moderator:
Dick said:
It's not only not correct. It has no content whatsoever. Give us some numbers. A Markov chain is a sequence of events where you have a potentially infinitely recurring state. This is one. There may be a more elementary way to solve this but I haven't thought of it.

Well, I looked at a previous problem in the homework. This is the probability of winning in exactly n tries in this game:

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110409_231023.jpg?t=1302408812

Last edited by a moderator:
Stop posting these blurry photobuckets and give me some straight answers. What is the probability of winning at n=1? That shouldn't even require much thought, much less calculation. Now n=2. You might have to think about that for a few seconds. Not much more. If you get that then do n=3. If I see another vague, blurry photobucket shot I'm out of here.

dick said:
stop posting these blurry photobuckets and give me some straight answers. What is the probability of winning at n=1? That shouldn't even require much thought, much less calculation. Now n=2. You might have to think about that for a few seconds. Not much more. If you get that then do n=3. If i see another vague, blurry photobucket shot I'm out of here.

Of course, you can look at each roll separately, and it's always 1/4. Right?

Shackleford said:
Of course, you can look at each roll separately, and it's always 1/4. Right?

Wow, you evaded any meaningful answer again. Yes, your probability of getting any given number is 1/4. Now tell me something about how that would translate into a probability of winning the game at any given n. Any n, you pick.

Let me give you an example for n = 4.

Given that in the zeroth try we got R0. In the first try, we can have only 3 allowed throws with probability 3/4. In the second try, you're not allowed to get either R0 or R1, so you have two allowed throws with probability 2/4. Again third try, you are not allowed to get R0 and R2, so again probability is 2/4. Finally in the 4th try, the only allowed throw is R0, with probability 1/4. So probability for winning in 4 throws is

(3/4)(2/4)(2/4)(1/4).

Now, use the same logic and find it for more numbers (n=1 is a slightly special case, so make sure you do that too)

Shouldn't it always be 2/4 for every k not equal to 1 or n?

3*(1/4)n*2n-2

Last edited:
I'm off just a bit.

## What is "Play the Probability Game: Test Your Luck!"?

"Play the Probability Game: Test Your Luck!" is a game that allows players to test their luck by making predictions about the outcomes of different events or scenarios.

## How do I play the game?

To play the game, you will be presented with a series of scenarios or events. You will then have to predict the likelihood of certain outcomes, ranging from highly probable to highly unlikely. You will earn points based on the accuracy of your predictions.

## What is the purpose of the game?

The purpose of the game is to have fun and challenge your understanding of probability. It can also help improve your critical thinking skills and decision-making abilities.

## Is there a correct answer for each prediction?

No, there is no correct answer for each prediction. The game is based on probability, so there are no definite outcomes. Your predictions may be more or less accurate, but the game is meant to be a fun and educational experience, not a test.

## Can I play this game with others?

Yes, you can play "Play the Probability Game: Test Your Luck!" with others. It can be a fun and interactive way to challenge and learn from each other's predictions.

• Calculus and Beyond Homework Help
Replies
1
Views
933
• Calculus and Beyond Homework Help
Replies
11
Views
2K
• Calculus and Beyond Homework Help
Replies
15
Views
3K
• Calculus and Beyond Homework Help
Replies
5
Views
2K
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
14
Views
3K
• Calculus and Beyond Homework Help
Replies
12
Views
6K
• Calculus and Beyond Homework Help
Replies
7
Views
2K
• Calculus and Beyond Homework Help
Replies
19
Views
3K
• Calculus and Beyond Homework Help
Replies
6
Views
2K