Question

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

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

Answer:

No, $P(A)
eq P(A|B)$