Hi, everyone :wave:. Newb to the forum here. Thanks in advance for taking a look at this!

this isn't homework, so i can't confirm if the answer is correct. I recently got on an elevator and noticed that the order in which people came onto the elevator is the same order in which they came off (i.e. first on, first off; last on, last off). I forgot most of my stats (but want to get back into it) and thought this would be a good exercise. Here's what I did:

extended the multiplication rule: the probability of P(a & b) = p(a|b) x p(b).

There was no need to calculate the odds of those getting ON were in any specific order, because that order is random. The odds are that they get off in the same fashion they got on was what mattered.

Therefore its simply probability for each person

Probability that person 1 gets off 1st = 1 in 5 chance = 20%
Probability that person 2 gets off 2nd = 1 in 4 chance = 25%
Probability that person 3 gets off 3rd = 1 in 3 chance = 33.3%
Probability that person 4 gets off 4th = 1 in 2 chance = 50%
Probability that person 5 gets off 5th = 1 in 1 chance = 100%

So = 20% x 25% x 33.3% x 50% x 100% = 0.83%


To confirm I took the factorial. If there are 5 people getting on, then the number of permutations in which they can get off is 5! = 5 x 4 x 3 x 2 x 1 = 120. Out of those 120 options, 1 of those options is getting off in the same pattern you got on; so its 1/120 = 0.83%


Is this right or did i just do it wrong in two different ways????

Yep, that's correct from both directions.