Question

A particular company has 51 employees. When the employees were asked how they get to work, 17 said they work from home, 20 drive alone, and 14 carpool. Assuming the employees are telling the truth, what is the empirical probability that an employee works from home? Write your answer as an exact fraction which is reduced as much as possible.

Answer 1

The empirical probability that an event A will occur is found by

`\begin{gathered} P(A)=(n(A))/(n(S)) \\ \text{ Where }n(A)\text{ is the number of times the event occurs and} \\ n(S)\text{ is the number of times the experiment is performed } \end{gathered}`

So, in this case, let A be the event in which an employee works from home. Then, we have:

`\begin{gathered} n(A)=17 \\ n(S)=51 \\ P(A)=(n(A))/(n(S)) \\ P(A)=(17)/(51) \\ \text{ Simplifying} \\ P(A)=(1\cdot17)/(3\cdot17) \\ \boldsymbol{P(A)=(1)/(3)} \end{gathered}`

Therefore, the empirical probability that an employee works from home is 1/3.