Probability that ƒ¿ º ƒÀ
If ƒ¿ and ƒÀ are subsets of {1,...,n}, what is the probability that ƒ¿ º
ƒÀ? Given that ƒ¿, ƒÀ are chosen independently of each other and with the
same probability.
I know that there are 2^n possible subsets of {1,...,n} (including the
empty set and the whole {1,...,n}) and if |ƒÀ| = k then there are 2^k
possible subsets of ƒÀ, which can be our ƒ¿.
I suspect (but I'm not 100% sure) that probability space Ħ has a size of
2^2n. If this is true I need to find the number of ways in which ƒ¿ can be
a subset of ƒÀ. I'm not really sure how to do this since I don't know the
number of elements in ƒÀ.
Can someone perhaps give me a little hint?
I'm so sorry if this problem is too trivial, I'm very much a beginner and
I find this to be pretty hard.
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