Respuesta :
Answer:
(a) [tex]P(A\cup T)[/tex] = 0.74.
(b) [tex]P(A^{c})[/tex] = 0.45.
(c) [tex]P(A^{c}\cup T^{c})[/tex] = 0.26.
Step-by-step explanation:
If events X and Y are two events (subset of a sample space S) and are not disjoint, then
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]
This is known as the addition rule or addition theorem.
The formula to compute the probability of neither X nor Y is:
[tex]P(X^{c}\cup Y^{c})=1-P(X\cup Y)[/tex]
The probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.
Complement of an event is, 1 – P.
Denote the events as follows:
A = a HRO has problems with absenteeism
T = a HRO has problems with turnover
The information provided is:
[tex]P(A)=0.55\\P(T)=0.41\\P(A\cap T)=0.222[/tex]
(a)
Compute the value of P (A ∪ T) as follows:
[tex]P(A\cup T)=P(A)+P(T)-P(A\cap T)\\=0.55+0.41-0.22\\=0.74[/tex]
Thus, the probability that a HRO selected from the group surveyed had problems with employee absenteeism or employee turnover is 0.74.
(b)
Compute the value of [tex]P(A^{c})[/tex] as follows:
[tex]P(A^{c})=1-P(A)\\=1-0.55\\=0.45[/tex]
Thus, the probability that a HRO selected from the group surveyed did not have problems with employee absenteeism is 0.45.
(c)
Compute the value of [tex]P(A^{c}\cup T^{c})[/tex] as follows:
[tex]P(A^{c}\cup T^{c})=1-P(A\cup T)\\=1-0.74\\=0.26[/tex]
Thus, the probability that a HRO selected from the group surveyed did not have problems with employee absenteeism nor with employee turnover is 0.26.
