Question

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)?
$\frac{1}{6}$
$\frac{1}{3}$
$\frac{2}{3}$
$\frac{5}{6}$

Explanation:

Step1: Recall the formula for independent events

For independent events \(X\) and \(Y\), \(P(X\cap Y)=P(X)\times P(Y)\)

Step2: Substitute the given probabilities

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

Step3: Calculate the product

\(\frac{1}{3}\times\frac{1}{2}=\frac{1\times1}{3\times2}=\frac{1}{6}\)

Answer:

A. \(\frac{1}{6}\)