# Probability of a random subset of Z

• MHB
• Statistics4win
In summary, the probability of selecting a proper subset of A from Z is equal to the number of proper subsets of A divided by the number of all subsets of Z. The probability of A and B having no common elements is equal to the probability of B being a subset of the complement of A.
Statistics4win
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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:
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 $A\cap B=\emptyset\iff B\subseteq Z\setminus A$.

## 1. What is the probability of getting a specific number in a random subset of Z?

The probability of getting a specific number in a random subset of Z is 1 divided by the total number of integers in the subset. For example, if the subset contains 10 integers, the probability of getting a specific number would be 1/10 or 0.1.

## 2. How is the probability of a random subset of Z calculated?

The probability of a random subset of Z is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This is known as the classical definition of probability.

## 3. What is the difference between a random subset of Z and a random sample of Z?

A random subset of Z is a subset of integers that is selected randomly and may contain repeated elements. A random sample of Z is a subset of integers that is selected randomly without any repeated elements. The probability of getting a specific number in a random sample of Z is higher compared to a random subset of Z.

## 4. Can the probability of a random subset of Z be greater than 1?

No, the probability of a random subset of Z cannot be greater than 1. This is because the probability is a measure of the likelihood of an event occurring, and it ranges from 0 to 1. If the probability is greater than 1, it means that the event is certain to occur, which is not possible in a random subset of Z.

## 5. How does the size of the subset affect the probability of a random subset of Z?

The size of the subset does not affect the probability of a random subset of Z. The probability is only dependent on the number of desired outcomes and the total number of possible outcomes. However, as the size of the subset increases, the probability of getting a specific number in the subset decreases, as there are more possible outcomes.

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