consider a situation in which $p(x)=\frac{4}{5}$ and $p(y)=\frac{1}{4}$. if $p(x$ and $y)$ is…

consider a situation in which $p(x)=\frac{4}{5}$ and $p(y)=\frac{1}{4}$. if $p(x$ and $y)$ is $=\frac{1}{5}$, which best describes the events?\nthey are independent because $p(x)cdot p(y)=p(x$ and $y)$.\nthey are independent because $p(x)+p(y)=p(x$ and $y)$.\nthey are dependent because $p(x)cdot p(y)=p(x$ and $y)$.\nthey are dependent because $p(x)+p(y)=p(x$ and $y)$.

consider a situation in which $p(x)=\frac{4}{5}$ and $p(y)=\frac{1}{4}$. if $p(x$ and $y)$ is $=\frac{1}{5}$, which best describes the events?\nthey are independent because $p(x)cdot p(y)=p(x$ and $y)$.\nthey are independent because $p(x)+p(y)=p(x$ and $y)$.\nthey are dependent because $p(x)cdot p(y)=p(x$ and $y)$.\nthey are dependent because $p(x)+p(y)=p(x$ and $y)$.

Answer

Explanation:

Step1: Calculate (P(X)\cdot P(Y))

$P(X)\cdot P(Y)=\frac{4}{5}\times\frac{1}{4}=\frac{4\times1}{5\times4}=\frac{1}{5}$

Step2: Compare with (P(X\ and\ Y))

We know (P(X\ and\ Y)=\frac{1}{5}), and since (P(X)\cdot P(Y) = P(X\ and\ Y)), the events are independent. The condition for two - events (X) and (Y) to be independent is (P(X)\cdot P(Y)=P(X\ and\ Y)).

Answer:

They are independent because (P(X)\cdot P(Y)=P(X\ and\ Y)).