I never took a course just on probability, sorry.

Anyway, let's say I have a cup with 4 differently colored chips (yellow, red, brown and turquoise). Now, for some strange betting game, I have to guess which colors come out for 10 rounds. I win if I can accurately guess all the colors that will come out for each run.

Now, I decide that, for the 10 times a color will be randomly picked from the cup, it will be yellow . So obviously...

1. yellow
2. yellow
3. yellow
4. yellow
5. yellow
6. yellow
7. yellow
8. yellow
9. yellow
10. yellow

According to probability, are the chances of me winning the game greater, equal or much less than if I choose alternating colors for my 10 guesses?

I calculated that the chances of me winning would be 1 out of 1048576, so I'm thinking it doesn't matter if I didn't use different color guesses. But, just to be sure, I'm right, right?

Probably.

I assume you're talking about theoretical probability. So, guessing yellow each time will give you a 1 out of 4 chance of getting it right. However, guessing a different color each time will also give you a 1 out of 4 chance of getting it right. So guessing each outcome to be the same is just as good as guessing differently.

However, in experimental probability, there are so many factors that can change the outcome that it would be almost impossible to predict the outcome. If, for example, you placed the yellow chip in the same place in the cup every time, you could easily pick that chip every time and "outsmart" theoretical probability.

That's the way I see it.

Also keep in mind that while 10 of yellow is 1 out of 1,048,576, any other combination is also 1 out of 1,048,576. We may tend to think that all yellow is less likely, but infact it is equal to any other result.

Excatly the same.

Are you taking into account the fact that there might not be an equal distribution of colors in the bag? Can we calculate the probability that there will be an equal distribution?

I was never very good at probablility.

It depends on whether you want a specific colour combination, eg. yellow red yellow red yellow red etc.

If you do, the chances are exactly the same as being all yellow. However if you mean by alternating colours you accept

yellow turquoise, yellow turquoise etc
or brown red brown red etc
or yellow brown yellow brown etc

then the chances will be higher to get alternating colours

wouldn't is also make a diffrence as to how many or each ship there are? If they all start out the same then the next time you dump then you have one less of whatever chip came out. so it would be slightly very slightly more probable to guess a more even distribution of chip colors.

for example:
if you say all yellow than:
yellow comes out first
not there is one less yellow than the other colors making it sligtly less probable that you get a yellow this time based on how many chips are in the cup total.





unless the point is you only use 4 chips and put them all back each time, then never mind.

Well he mentioned using 4 chips so I'd assume he'd be putting them back straight away or it would be a rather silly question :p