Suppose that 100 men check their hats at a party, and the hats are randomly returned to them at the end. Is it more likely than not that at least one man will get his own hat back? Is it more likely than not that at least two men will get their own hats back? Explain.

Question

Reina Duran

Mathematics

16 March, 11:53

Suppose that 100 men check their hats at a party, and the hats are randomly returned to them at the end. Is it more likely than not that at least one man will get his own hat back? Is it more likely than not that at least two men will get their own hats back? Explain.

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Hugh Dickerson · Answer 1

It is highly unlikely that we could find higher probability that hats would be returned correctly.

We can look at the ratio 1:100

Lets look at a 1/4 of the data

1:25

25-1=24 ratio is 1:25

fraction is 1/25

Now we x 4 on the 1/4 chance that you were the first 1/4 to come to the party first and you are also the 1/4 that left first.

and get 4/25

We can try the odds of the following;

Age 1/3 based on a large party spanning 3 generations possibly.

Also style 1/5

5 party styles this presents 1/2 based on randomness.

= x5 and x 3

= Age 5/15 Style 3/15 and we get 8/15

But when we apply this to the orderly of arriving first last to leave etc.

We see that hats would get mixed up, so therefore the 8/15 added and converted to 1/100 is simply divided by 0.06/6.66 x 8

Here we have 8 / (100/15 = 6.66 x 8) = 8/53.28 and can see that it is in simplest form at 8/53. Being possible decimal 0.150943396 based on random selective. But 1/100 stays the only calculation possible for pure random.