MHB Probability of a random subset of Z

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To calculate the probability of a random subset B of Z being a proper subset of A, the number of proper subsets of A must be divided by the total number of subsets of Z. Since A has four elements, it has 15 proper subsets. The total number of subsets of Z, which has ten elements, is 2^10 or 1024. For the second part, the condition A ∩ B = Ø means that B must be a subset of the complement of A within Z, which consists of the elements {5, 6, 7, 8, 9, 10}. Understanding these probabilities requires recognizing the equal likelihood of selecting any subset from Z.
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I'm stuck in this question, could someone give me a hand?

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

a) $$P (B⊂A)$$ B is a proper subset of A
b) $$P (A∩B = Ø)$$ A intersection B =empty set
Appreciate
 
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Statistics4win said:
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 $A\cap B=\emptyset\iff B\subseteq Z\setminus A$.
 
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