Hello Every body I'm trying solve this problem ADASEA — Ada and Island I tried to understand what it want but I can't.
their is some meanings that i can't understand :
-- considering equal probability for all coordinates
-- so she has asked you to tell her the expected size of island .
All I want is to know what each word mean and if some one could explain the last two test Cases . I Would be Grateful .
The Last thing I Want to do is to thank Errichto for his Video Algorithms Lecture #1 — Sums and Expected Value.
Good day to you,
to "ADASEA":
a)"considering equal probability for all coordinates" .. this means, that if you jump on NxM field, you have equal probability you landed on any of 0 <= x < N / 0 <= y < M coordinates... so for example having 1x5 field, you have 20% for each of the coordinates (0-0,0-1,0-2,0-3,0-4)
b) Here is what "expected value" means (necessary for this problem).
c) So in the end, the expected size of island is something like "weighted average" of size of island she will land to (so basically size of island she lands to times the probability of the landing)
So this is easy.. she has 100% chance to fall on the only island which is there, which has size 1, so it is expected that size of island shell fall to is 1 [obviously]
So here she have 1/16 to fall into any place.. There is only one island of size 6... so you have 6 chances 1/16 to fall into island of size 6, otherwise 10 chances of 1/16 to fall into island of size 0 .. that means the expected size is 6*6*1/16 == 9/4
Good Luck!
First of All thank you very much and the second thing is that when she has 6 chances to fall into inland and 6 chances that she doesn't fall into island so that's why 6 ^ 2 * 1 / 16 ?? and second thing their is any material that's makes me understand basic probability as i'm confused is that okay that i'm confused, is that normal !!