system only show 1 and 0 But there is possble have error whe

system only show 1 and 0. But there is possble have error. when is error to 1 then it will show 0. if 0 have error then it show 1. possible have error of both is 0.08. Possible to generate 1 is 55% and 0 is 45% what is probabilty to system show 1 or 0?

the question is like this and im not sure right way to do it. i was thinking if i find probabilty 1. then i did 0.45 x 0.08 + 0.55 but not sure this is right can you help me?

Solution

Here conditional probability will be used. Let A shows the event that system generate 1, B shows the event that system generate 0. So

P(A)=0.55

P(B)=0.45

Now the probability that system show 0 (that is error), given that system generate 1 is

P(show 0| A)=0.08

And the probbaility that system show 1, given that system generate 1 is

P(show 1|A)=1-0.08=0.92

Now the probability that system show 1 (that is error), given that system generate 0 is

P(show 1| B)=0.08

And the probbaility that system show 0, given that system generate 0 is

P(show 0|B)=1-0.08=0.92

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Now from the condiional probability rule: Probability that system will show 1 is

P(show 1)= P(show 1| A) *P(A)+P(show 1| B) *P(B)=0.92*0.55+0.08*0.45=0.542

And Probability that system will show 0 is

P(show 0)= P(show 0| A) *P(A)+P(show 0| B) *P(B)=0.08*0.55+0.92*0.45=0.458

So the probability that system will show 0 or 1 is

P(show 0 or show 1)=0.458+0.542=1

Note:

Logically system can shows either 1 or 0 , so the probability that system will show 1 or 0 is 1. No need to do above calculations. Calcualtions are requried when you need probabiltiy that system will show 1. Or you need the probability that system will show 0.