Answer:
The probability of an operating system error given that a failure has ocurred is P(O/E)= 0.19
Step-by-step explanation:
Hello!
There are three different sources of error when a computer system fails:
D: disk drive error. ⇒ P(D)= 0.50
M: computer memory error. ⇒P(M)= 0.20
O: operating systems error. ⇒ P(O)= 0.30
According to the component perdormance standard:
The probability of failure "E", given that there is a disk drive error is P(E/D)= 0.40
The probability of failure "E", given that there is a computer memory error is P(E/M)= 0.6
The probability of failure "E", given that there is a operating system error is P(E/O)= 0.25
You need to calculate the probability of an operating system error given that a failure has ocurred, symbolically:
P(O/E)
[tex]P(O/E)= \frac{P(OnE)}{P(E)}[/tex]
To reach the probability of the marginal E you have to add all intersections between the event "E" and the events "D", "M" and "O"
D M O Total
E: P(E∩D); P(E∩M); P(E∩O); P(E)
Using the formula of the conditional probability I'll clear all three intersections using the known probabilities:
General formula: [tex]P(A/B)= \frac{P(AnB)}{P(B)}[/tex] ⇒ [tex]P(AnB)= P(A/B)*P(B)[/tex]
P(E∩D)= P(E/D)*P(D)= 0.4*0.5= 0.2
P(E∩M)= P(E/M)*P(M)= 0.6*0.2= 0.12
P(E∩O)= P(E/O)*P(O)= 0.25*0.3= 0.075
P(E)= P(E∩D) + P(E∩M) + P(E∩O)= 0.2+0.12+0.075= 0.395
[tex]P(O/E)= \frac{P(OnE)}{P(E)} = \frac{0.075}{0.395}= 0.189 = 0.19[/tex]
I hope it helps!
