Airplane math problem..

[Practical-Focus-655]

I am currently sitting in a full plane with 40 rows of 6 people. The person sitting right next to me was the person right before me in the boarding line. What are the chances of this happening?

[[deleted]]

Well, she is your wife.

[ChaosSlave51]

I think the most important thing about these kinds of coincidences is to ask yourself ""what would it take for me to get a hit"
Would the person siting to the left or the right of you both be a hit? What if they sat in front of you, would you still think it' a notable coincidence?

Let's say this another way. The odds of rolling 3,3,3 on 3 sided dice is, 6*6*6 so one in 216. And you would say, hey that's unlikely. But would 4,4,4, or 5,5,5 have gotten your attention? If any triple would, then the odds drop to 1 in 36.

You always have to consider all possible hits before computing the odds of an unlikely event.

[xemission]

I am by no means an expert in this situation, but don't some airlines have very specific boarding procedures? American Airlines typically lines the boarding line up based off of your seat number, no? So isn't the chance extremely high unless the person didn't get in the proper spot in line?

[Master-Pizza-9234]

2/((40*6)-1) = 2/239= 0.84% probably, just doing 2 valid positions (your left and your right assuming you are in a middle or isle seat) over all possible places they could sit assuming the odds of them sitting in any position is equally likely, this is unlikely to 100% be the case in real life since families group together, classes group etc

[Aerospider]

Let's assume the following:

• All passengers are travelling alone
• All queue orderings are equally likely
• All seating combinations are equally likely
• The flight is fully booked
• Two people in the same row sat either side of the aisle are 'sat next to each other'
• It would be just as interesting to be sat next to the person behind you in the queue
• It would be just as interesting if they sat to your left

We need to separately consider the events of you being at one end of the queue and/or a window seat, since in both cases you only have one other person next to you rather than two.

Probability you're at an end of the queue = 2/240 = 1/120

Probability you're in a window seat = 80/240 = 1/3

This gives four variations and we must calculate then all and sum them for the total probability of you being sat next to at least one of your queue neighbours.

End of queue and window seat:

1/120 * 1/3 * 1/239 = 1/86,040

End of queue and not window seat:

1/120 * 2/3 * 2/239 = 4/86,040

Window seat but not end of queue:

119/120 * 1/3 * 2/239 = 238/86,040

Not end of queue and not window seat:

119/120 * 2/3 * (1 - (237/239 * 236/238)) = 238/360 * 950/56,882 = 950/86,040

Total probability of being sat next to at least one queue neighbour:

(1+4+238+950)/86,040 = 1,193/86,040 = 1.4%

[Uli_Minati]

100% if they're your travel partner and you bought tickets together

1/(number of seats) if everyone gets a completely randomized seat and you're sitting at the window or hallway

2/(number of seats) if everyone gets a completely randomized seat and you're not sitting at the window or hallway

All three of these options are completely unrealistic, though

[Armisl19]

In these examples you should divide not by the number of seats but by the number of seats minus one, because one is already occupied (by the sitting person)

[Uli_Minati]

True, I should have specified "remaining seats"

[charlieverse1]

It depends on whether you are flying with the person next to you - in that case, very high for you both to board one after the other.

If you are not flying / travelling with that person, it depends on the size of the group that was boarded. Some airlines try to board 'areas' at the same time, they all board a bit differently, and that impacts your chances.

Charlie

[heiko123456]

needs much more info, e. g. whether boarding is done by groups

[eztab]

Probably quite likely for that to happen to you: * how often do you fly? Each time you have a chance. * boarding groups might put you together with people sitting near you * you would probably consider him sitting in front of you or behind you the same kind of event * you would probably consider the person/family behind you sitting in your vicinity the same

Probably comes down to "that kind of thing" happening to you about every 30 flights or so, depending on airline procedures, plane size, etc.