Question

events a and b are independent. the probability of a occurring is \frac{2}{5}. the probability of b occurring is \frac{1}{4}. what is p(a and b)? \frac{1}{10} \frac{1}{3} \frac{5}{8} \frac{13}{20}

Explanation:

Step1: Recall the formula for independent events

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\)

Step2: Substitute the given probabilities

Given \(P(A)=\frac{2}{5}\) and \(P(B)=\frac{1}{4}\), then \(P(A\cap B)=\frac{2}{5}\times\frac{1}{4}\)

Step3: Calculate the product

\(\frac{2}{5}\times\frac{1}{4}=\frac{2\times1}{5\times4}=\frac{2}{20}=\frac{1}{10}\)

Answer:

\(\frac{1}{10}\) (corresponding to the first option)