MHB Probability of a random subset of Z

  • Thread starter Thread starter Statistics4win
  • Start date Start date
  • Tags Tags
    Probability Random
Statistics4win
Messages
1
Reaction score
0
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
 
Last edited:
Mathematics news on Phys.org
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 $A\cap B=\emptyset\iff B\subseteq Z\setminus A$.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top