# ..

..
(edited 3 weeks ago)
https://isaacphysics.org/questions/poisson_woodland?stage=a_level
Please could I have some help with part e. I tried to find the answer by finding the probability of it containing exactly 8 trees, the probability of it containing more than 8 trees and the probability of it containing less than 8 trees. I multiplied all of these together (including squaring the probability of it containing exactly 8), but when I submitted my answer, Isaac told me to consider the number of ways that this could be done.
I’m not sure how to account for this. Is this a case of conditional probability? Any help would be gratefully received. Thank you in advance.

Not really worked it through, but Id imagine is like the nCr type argument when you do binomial, so if youve worked out the probability that 2 out of 4 are 8, then how many combinations of 2 out of 4 are there and similarly for the other condition.
https://isaacphysics.org/questions/poisson_woodland?stage=a_level
Please could I have some help with part e. I tried to find the answer by finding the probability of it containing exactly 8 trees, the probability of it containing more than 8 trees and the probability of it containing less than 8 trees. I multiplied all of these together (including squaring the probability of it containing exactly 8), but when I submitted my answer, Isaac told me to consider the number of ways that this could be done.
I’m not sure how to account for this. Is this a case of conditional probability? Any help would be gratefully received. Thank you in advance.

It's not conditional probability. If we write E for equals 8, L for less than 8 and M for more than 8, then

P(E)^2 P(L) P(M) would be the probability that the first 2 regions = 8, the 3rd region is < 8 and the 4th region is > 8 (or to put it another way, that EELM occurred in that order).

You need to account for all possible arrangements, e.g. EEML, ELME etc. (Hopefully it's clear that each arrangement will have the same probability, so at least you don't have to keep working that out for each arrangement).