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

Answer

Explanation:

Step1: Recall probability formula for independent events

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

A. (\frac{1}{10})