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Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively. A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A ∪ F) = _____________.
(A) 0.07
(B) 0.10
(C) 0.20
(D) 0.13 (E) 0.17

Respuesta :

JeanaShupp

Answer: 0.23

Step-by-step explanation:

Given : F is the event "works in the finishing department;"

and A is the event "is absent excessively."

Given : 10% of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively.

i.e. P(A)= 0.20 ;  P(F)=0.10 ; P(A ∩ F) = 0.07

We know that [tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]

Then,

[tex]P(A\cup F)=P(A)+P(F)-P(A\cap F)\\\\\Rightarrow\ P(A\cup F)=0.20+0.10-0.07=0.23[/tex]

Hence, the required answer is [tex]P(A\cup F)=0.23[/tex]

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