Whateverist:
It seems like you have the same solution paths as me for 3 and 4 people, but you're assuming the probability of each combination is the same. Sadly, they are not. So simply counting them isn't enough. That's what makes this problem harder.
For example, with 3 people, it must be 2, 1, 3
Player 1 can pick either name 2 or name 3. He can't pick his own. So the probability he picks name 2 is 1/2.
You can write it out explicitly including his own number, but you get the same result, as if it wasn't in there:
Prob(pick 2 on first try) + prob(pick own number)*prob(pick 2 on second try)
=1/3 + 1/3 * 1/2
=1/3 + 1/6
=1/2
So now player 2 must pick number 1. The numbers left are 1 and 3. So it's a straightforward 1/2.
Combining these gives 1/2 * 1/2 = 1/4
Similarly for the two lines for 4 people.
@aractus: Thanks, I'll have a look at that lot later.
It seems like you have the same solution paths as me for 3 and 4 people, but you're assuming the probability of each combination is the same. Sadly, they are not. So simply counting them isn't enough. That's what makes this problem harder.
For example, with 3 people, it must be 2, 1, 3
Player 1 can pick either name 2 or name 3. He can't pick his own. So the probability he picks name 2 is 1/2.
You can write it out explicitly including his own number, but you get the same result, as if it wasn't in there:
Prob(pick 2 on first try) + prob(pick own number)*prob(pick 2 on second try)
=1/3 + 1/3 * 1/2
=1/3 + 1/6
=1/2
So now player 2 must pick number 1. The numbers left are 1 and 3. So it's a straightforward 1/2.
Combining these gives 1/2 * 1/2 = 1/4
Similarly for the two lines for 4 people.
@aractus: Thanks, I'll have a look at that lot later.
Feel free to send me a private message.
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Please visit my website here! It's got lots of information about atheism/theism and support for new atheists.
Index of useful threads and discussions
Index of my best videos
Quickstart guide to the forum