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?\na. $\frac{3}{100}$\nb. $\frac{1}{20}$\nc. $\frac{1}{12}$\nd. $\frac{3}{5}$\ne. $\frac{13}{20}$

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?\na. $\frac{3}{100}$\nb. $\frac{1}{20}$\nc. $\frac{1}{12}$\nd. $\frac{3}{5}$\ne. $\frac{13}{20}$

Answer

Explanation:

Step1: Identify the conditional - probability formula

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

Step2: Calculate the conditional probability

Substitute the given values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{1}{20}}{\frac{3}{5}}$. When dividing by a fraction, we multiply by its reciprocal: $\frac{1}{20}\times\frac{5}{3}=\frac{1\times5}{20\times3}=\frac{5}{60}=\frac{1}{12}$.

Answer:

C. $\frac{1}{12}$