the probability that an employee at a company lives more than 10 miles from the office is $\frac{3}{5}$. the…

the probability that an employee at a company lives more than 10 miles from the office is $\frac{3}{5}$. the probability that an employee who lives more than 10 miles from the office bikes to work is $\frac{1}{20}$. what is the probability that an employee bikes to work given that the employee lives more than 10 miles from the office? a. $\frac{3}{100}$ b. $\frac{1}{20}$ c. $\frac{1}{12}$ d. $\frac{3}{5}$ e. $\frac{13}{20}$

the probability that an employee at a company lives more than 10 miles from the office is $\frac{3}{5}$. the probability that an employee who lives more than 10 miles from the office bikes to work is $\frac{1}{20}$. what is the probability that an employee bikes to work given that the employee lives more than 10 miles from the office? a. $\frac{3}{100}$ b. $\frac{1}{20}$ c. $\frac{1}{12}$ d. $\frac{3}{5}$ e. $\frac{13}{20}$

Answer

Explanation:

Step1: Identify given probabilities

Let $A$ be the event that an employee lives more than 10 miles from the office, $P(A)=\frac{3}{5}$. Let $B$ be the event that an employee bikes to work. We are given the conditional - probability $P(B|A)=\frac{1}{20}$. The question asks for $P(B|A)$.

Step2: Recall conditional - probability formula

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$, but in this case, we are already given the value of $P(B|A)$ which is the probability that an employee bikes to work given that the employee lives more than 10 miles from the office.

Answer:

B. $\frac{1}{20}$