Undergrad Probability help

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Any help will be appreciated

[sudden kindle]

For the airline passenger problem.
Consider P1 goes to seat Sk. Now Pk will got to any seat either it will be S1 or something from Sk+1 to Sn. If you chalk this out in the end there will be only two possibilities left for Pn. Either he will have his seat free or his seat is occupied and he'll have to sit at seat S1.

So total probability = P(Pn has his seat empty) =
(1/2)

In general for kth passenger from the last the P(his seat is free) = k/(k+1)

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The answer given is (n-2)/(2n-2)

[sudden kindle]

It seems wrong
Check for N = 3 let's say
The answer should be 1/2(check by drawing out all the possibilities )which doesn't come from this formula

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It seems right for N =3. If you put 3 in the formula, you get 1/4 which is the same as when we count the possibilities

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You're right though. If I put n =4, the formula doesn't satisfy

But I think I've found the right answer. Tried till n =6 and I can see a pattern

Answer is (n-2)/(n-1)^2

[mellow compass]

These are some really interesting questions

Any progress on the first one?

(please ping)

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Unfortunately no

[mellow compass]

Dang

I basically understood how to solve it but I really don't know how to explain it

also I'm busy right now

[mellow compass]

This is nice, but I personally wouldn't have given them this explanation if I had it

This is because this just tells them the reasoning, which is better than just telling the answer, but is not as good as guiding them through it

[tiny shell]

ok i'll delete it then and prompt them with a question

[mellow compass]

But of course giving them an explanation is better than them not solving it ever

[tiny shell]

@spare widget for the first problem do casework on what pi_k can be equal to