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Probability of a random subset of Z


New member
Apr 23, 2019
I'm stuck in this question, could someone give me a hand?

Question 9:
Let \(\displaystyle A = (1,2,3,4)\) and \(\displaystyle Z = (1,2,3,4,5,6,7,8,9,10)\), if a subset B of Z is selected by chance calculate the probability of:

a) \(\displaystyle P (B⊂A)\) B is a proper subset of A
b) \(\displaystyle P (A∩B = Ø)\) A intersection B =empty set

Last edited:


Well-known member
MHB Math Scholar
Jan 30, 2012
if a subset $B$ of $Z$ is selected by chance
This may mean different things. What are probabilities of selecting individual subsets if $Z$? If all such probabilities are equal, i.e., if each subset is equally likely, then $P(B\subset A)$ equals the number of proper subsets of $A$ divided by the number of all subsets of $Z$. For the number of subsets see Powerset in Wikipedia. For b) note that $A\cap B=\emptyset\iff B\subseteq Z\setminus A$.