# Probability of a random subset of Z

#### Statistics4win

##### New member
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

Appreciate

Last edited:

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
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 $A\cap B=\emptyset\iff B\subseteq Z\setminus A$.