events a and b are independent. the probability of a occurring is $\frac{2}{5}$. the probability of b…

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 $p(a \text{ and } b)$?\n$\frac{1}{10}$\n$\frac{1}{3}$\n$\frac{5}{8}$\n$\frac{13}{20}$

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 $p(a \text{ and } b)$?\n$\frac{1}{10}$\n$\frac{1}{3}$\n$\frac{5}{8}$\n$\frac{13}{20}$

Answer

Explanation:

Step1: Recall probability - rule for independent events

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

Step2: Substitute given probabilities

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

Step3: Calculate the product

$\frac{2}{5}\times\frac{1}{4}=\frac{2\times1}{5\times4}=\frac{2}{20}=\frac{1}{10}$.

Answer:

A. $\frac{1}{10}$