[Guest]

Three people are wearing different hats.

If they exchange their hats in random, what is the chance that each of them would get a hat that is not their own?

[Guest]

Lets say the hats are 1,2 and 3 for the corresponding persons.

The only ways in which none would have the same hat after the exchange is 312 and 231.

Two possible cases out of 6 possible combinations in which hats may be rearranged.

So the probability is 1/3

[Guest]

Lets say the hats are 1,2 and 3 for the corresponding persons.

The only ways in which none would have the same hat after the exchange is 312 and 231.

Two possible cases out of 6 possible combinations in which hats may be rearranged.

So the probability is 1/3

You can't exchange a hat with yourself, I don't know if 321 is a possibility...

[Guest]

Three people are wearing different hats.

If they exchange their hats in random, what is the chance that each of them would get a hat that is not their own?

The probability that the first gets a different hat is 2/3

The probability that the second and third get different hats is 1/2

therefore the total probability is 2/3 * 1/2 = 1/3

[Guest]

Three people are wearing different hats.

If they exchange their hats in random, what is the chance that each of them would get a hat that is not their own?

if they are wearing their own hats to begin with, and do one random exchange, then the probability is 100%.

[Guest]

assuming that only one swap is made and you can not swap with your self then there is a 100% chance of getting a diferent hat, and if more then 1 trade is made there are three possible hats you can recive, only one of which is yours, so one out of three or 1/3 is your probibilty.