events x and y are independent. the probability of x occurring is $\frac{1}{3}$. the probability of y…

events x and y are independent. the probability of x occurring is $\frac{1}{3}$. the probability of y occurring is $\frac{1}{2}$. what is p(x and y)?\n$\frac{1}{6}$\n$\frac{1}{3}$\n$\frac{2}{3}$\n$\frac{5}{6}$

events x and y are independent. the probability of x occurring is $\frac{1}{3}$. the probability of y occurring is $\frac{1}{2}$. what is p(x and y)?\n$\frac{1}{6}$\n$\frac{1}{3}$\n$\frac{2}{3}$\n$\frac{5}{6}$

Answer

Explanation:

Step1: Recall probability formula for independent events

For independent events $X$ and $Y$, $P(X\text{ and }Y)=P(X)\times P(Y)$.

Step2: Substitute given probabilities

Given $P(X)=\frac{1}{3}$ and $P(Y)=\frac{1}{2}$, then $P(X\text{ and }Y)=\frac{1}{3}\times\frac{1}{2}$.

Step3: Calculate the product

$\frac{1}{3}\times\frac{1}{2}=\frac{1\times1}{3\times2}=\frac{1}{6}$.

Answer:

A. $\frac{1}{6}$