Messages relating to the status of an industrial system are transmitted to a monitoring station via an internal transmission network. During periods of low network traffic, 1.2% of these messages have transmission errors, but during periods of heavy network traffic the error rate is 4.7%.
Given that the traffic levels are low for 78% of each day, what is the probability that a randomly chosen message was transmitted during a high traffic period and also had a transmission error?
I dont know why, but i am having problems with this question.
so far i have my events as:
let "E" be the event "error has occurred"
Let "T" be the event "traffic is low"
Pr(T)=0.78
Pr(E|T)=0.012
Pr(E|¯T)=0.047
Is this correct so far?
UPDATE
So the answer is 0.01034, Thanks.
What is the proportion of messages in the last question that will have a transmission error?
Pr(E)=Pr(ET U E¯T)
=Pr(E|T) Pr(T) + Pr(E|¯T) Pr(¯T)
=0.012*0.078+0.047*0.22
=0.0197
What is the probability that a message from the first question which has a transmission error was transmitted during a period when the traffic levels were high?
Pr(¯T|E)=[Pr(E|¯T) Pr(¯T)]/Pr(E)
=(0.047*0.22)/0.0197
=~0.5249
Please tell me these are correct :)
Yes, it's correct so far. All you need is $P({\overline T})=1-P(T)$ and then the answer is $P(E,{\overline T})=P(E|{\overline T})\times P({\overline T})$