Question

probability and statistics
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 \text { and } y ) \\)?

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:

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