Respuesta :
Answer:
There is a 40% probability that an employee selected from the group surveyed had problems with either absenteeism or turnover.
Step-by-step explanation:
We can solve this problem building the Venn's diagram of these probabilities.
I am going to say that
The set A are those employees who had problems with absenteeism.
The set B are those employees who had problems with turnover.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a represents those that had problems with absenteeism but not work turnover and [tex](A \cap B)[/tex] are those who had problems with both these things.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
We start finding the values from the intersection of these sets:
Suppose that 40% of the employees had problems with both absenteeism and turnover.
This means that [tex]A \cap B = 0.4[/tex].
50% had problems with turnover
This means that [tex]B = 0.5[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]0.50 = b + 0.4[/tex]
[tex]b = 0.10[/tex]
70% of the employees had problems with absenteeism
This means that [tex]A = 0.7[/tex]
[tex]A = a + (A \cap B)[/tex]
[tex]0.70 = a + 0.4[/tex]
[tex]a = 0.30[/tex]
Use this information to find the probability that an employee selected from the group surveyed had problems with either absenteeism or turnover.
This is
[tex]P = a + b = 0.30 + 0.10= 0.40[/tex]
There is a 40% probability that an employee selected from the group surveyed had problems with either absenteeism or turnover.
