and how long employees have been at the company. suppose an employee is selected from this company at…

and how long employees have been at the company. suppose an employee is selected from this company at random. let event a = work weekends and event b = worked less than 5 years. are events a and b independent? mark and return

and how long employees have been at the company. suppose an employee is selected from this company at random. let event a = work weekends and event b = worked less than 5 years. are events a and b independent? mark and return

Answer

Explanation:

Step1: Calculate $P(A)$

$P(A)=\frac{\text{Number of employees who work weekends}}{\text{Total number of employees}}=\frac{35}{50}=\frac{7}{10}$

Step2: Calculate $P(A|B)$

$P(A|B)=\frac{P(A\cap B)}{P(B)}$. First, $P(A\cap B)=\frac{30}{50}$, $P(B)=\frac{35}{50}$. Then $P(A|B)=\frac{\frac{30}{50}}{\frac{35}{50}}=\frac{30}{35}=\frac{6}{7}$.

Step3: Check independence

Since $\frac{7}{10}\neq\frac{6}{7}$, i.e., $P(A)\neq P(A|B)$, events $A$ and $B$ are not independent.

Answer:

No, $P(A)\neq P(A|B)$