The random hats
A group of 100 men, all wearing hats, throw them to the air at the same time, letting them fall, and then pick one random hat from the floor.
Some of them will pick their own hat, and some will pick the wrong hat. But what is the EXPECTED number of men that pick the RIGHT hat (their own)?
Obviously, 50%? (50 men on average end up with the right hat, 50 with the wrong one)
Let's try with a smaller group - 4 men. Will 2 men on average get back their own hat?
Listing all the 24 (4!) possible, equally likely, permutations of the hats, it is not difficult to find that:
Some of them will pick their own hat, and some will pick the wrong hat. But what is the EXPECTED number of men that pick the RIGHT hat (their own)?
Obviously, 50%? (50 men on average end up with the right hat, 50 with the wrong one)
Let's try with a smaller group - 4 men. Will 2 men on average get back their own hat?
Listing all the 24 (4!) possible, equally likely, permutations of the hats, it is not difficult to find that:
- Only in 1 case (4%), they all get the right hat back
- In 6 cases (25%), 2 of them get the right hat back
- In 8 cases (33%), only 1 of them gets the right hat back
- In 9 cases (38%), NONE of them gets the right hat back
posted by DS at 6:17 PM
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