For the life of me I can't figure out how to solve this and I am in "dire" need of the answer.

"An object randomly changes between five different colors once a day. A person randomly guesses the objects color twice a day (not the same guess in one day). What are the chances that the person WON"T guess the objects color after 22 days?"

I came up with .0061%

Please give me a hand.

I dont see what you mean!

"not the same guess in one day" as in the person cannot guess "green" twice in one day, but has to guess two different colors.

I assume at least he knows what the five possible colors are, so he's not guessing aqua and chartreuse while the object switches between green red blue orange and purple. Absurd problem otherwise. So, the object changes color each day and stays the same color throughout the day, it might be blue on day 1 then red on day 2, etc? Seems like the hard part here is understanding what the problem is. Could be stated more clearly but I think I understand.

Ok so he makes two (different) guesses per day, meaning on any given day 2/5 chance of guessing the correct color for the day. But you want the probability he guesses incorrectly for 22 days straight. On any given day he has a 3/5 chance of not guessing correctly, so 22 straight days of never guessing right is (3/5)^22 = .00001316.

so that would be .0013%?


it makes sense, but just to make sure, id love if other would confirm.

Multiply by 100 to convert a probability to a percentage, so yes.

I confirm!(but why 22 days please?)

my friend and i have been guessing another friends shirt for 22 days. he only wears 5 different shirts, and we have never gotten it right. we are a statistical anomaly.

I thought the word problem i gave seemed simpler to explain though, any way, thats interesting. and for the record, the answer i gave in my question on my first post was for 19 days not 22, so i did do the math right. sorry this may not make too much sense as im super tired but hey.... anyway, thanks much

The math assumes your friend is choosing shirts randomly. He may be choosing strategically based on what he thinks you will do. The math also assumes you are guessing randomly, which is basically impossible unless you are using a randomizing mechanism and not just guessing. With a non-random shirt choice, and a non-random "guess" it's possible you will never get it right.

This makes a nice Nash equilibrium example, kind of like rock paper scissors.

I don't think you took into account that the color randomly changes once a day. That gives you a 1/2 chance of getting it right each day, so your chance of getting it wrong 22 days in a row is (1/2)²² or 1 in 4,194,304.

I think they just meant he wears a different shirt each day, for the entire day, and they get two guesses (they each guess). So it's 2/5 they get it right on any given day.

Yeah, different from the day before. That's what "change" means. You can't wear the same shirt 2 days in a row if you change it every day. It is 2/4 = 1/2 for each day.

I guess I assumed there was not a condition that the shirt must be different from the day before, because the problem statement originally said a random choice from the 5 available colors.

The OP should clarify that one.

He didn't say a random choice of 5 colors, he said it "randomly changes between 5 different colors once a day". The key is that it must change. Seems clear enough to me.

I will postulate that a guy who only has 5 shirts, probably occasionally wears 'em two days in a row.

Also, if betting on this, I would casually find out the laundry day of the guy. That will give you some predicability.

So if there were 6 t shirts and 14 days there would be a 34% chance? that seems awfully high too me.

If your guesses are random between the 5 colors (like OP said) it doesn't matter if the objects color changes or doesn't change at all for 22 days?

What if the color changes at noon and you randomly guess 2 times pre-noon (chance increases to 7/10)?

It doesn't say that you guess randomly out of 5 colors. That would be foolish.


That's not the problem, but you have to read the whole thread to realize that.

Your friends are playing a practical joke on you. They want to see how long you will take for you to get it. Your co-guesser is supplying Mr. Shirts with "inside information." This is a much more likely explanation than guessing wrong every day for 22 days.

http://www.youtube.com/watch?v=8c1BQkKUsx0