Timeline for Taking Seats on a Plane
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2021 at 7:58 | comment | added | user851668 | @DanielV Thanks! But how can I intuit $p_{k}={1\over n}+p_2{1\over n-1}+p_3{1\over n-2}\dots+p_{k-1}{1\over n-k}$? I still don't understand where this expression hails from! It feels like it appeared from left field! Can you de-mystify this to a 16 y.o.? | |
| Aug 23, 2021 at 11:49 | comment | added | DanielV | @KSLLF $1/n$ is the probability that the first person sits in seat $k$. The probability that person $j$'s seat is taken is $p_j$, and there are are $(n - j + 1)$ seats then he will choose from, $1$ of them is person $k$'s seat. | |
| Aug 23, 2021 at 7:58 | comment | added | user851668 | @DanielV 2. I know that "each term (except the first)" is "the probability that person j's seat is taken and he sits in seat k". But why's this $p_j \cdot (n - j + 1)^{-1}$? | |
| Aug 23, 2021 at 7:57 | comment | added | user851668 | 1. In your equation for $p_k$, what does $1/n$ (the first term) signify? Pls edit your answer to clarify. | |
| Aug 1, 2021 at 18:04 | comment | added | DanielV | Just to clarify, each term (except the first) is "the probability that person j's seat is taken and he sits in seat k", $p_j \cdot (n - j + 1)^{-1}$ , which are a complete list of ways person k's seat could be taken and all of them are disjoint, so it is correct to add them. | |
| Feb 1, 2021 at 9:56 | review | Late answers | |||
| Feb 1, 2021 at 10:11 | |||||
| Feb 1, 2021 at 9:39 | history | answered | user43170 | CC BY-SA 4.0 |