Question

A computer technician notes that 45% of computers fail because of the hard drive, 15%because of the monitor, 22% because of a disk drive and 18% because of the microprocessorIf the problem is not because of the disk drive, what is the probability that it is in the harddrive?

Answer 1

You have the following predictions

`\begin{gathered} P(X=HDrive)=0,45 \\ P(X=Monitor)=0.15 \\ P(X=DDrive)=0.22 \\ P(X=Microprocessor)=0.18 \end{gathered}`

Now, you need to now the probabily that your computer fails by the hard drive after discard the disk drive option, so it means is the conditional probability

`P(X=HDrive|X\\e Drive)=P(X=HDrive|X=HDrive,or,Monitor,or,Microprocessor)`

Remember that

`P(A|B)=(P(A\cap B))/(P(B))`

Then the probability that you need is the following

`(0.45)/(0.45+0.15+0.18)=(0.45)/(0,78)\approx0.5769`

The answer is 0,5769