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?

Respuesta :

You have the following predictions

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

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

[tex]P(X=HDrive|X\ne Drive)=P(X=HDrive|X=HDrive,or,Monitor,or,Microprocessor)[/tex]

Remember that

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

Then the probability that you need is the following

[tex]\frac{0.45}{0.45+0.15+0.18}=\frac{0.45}{0,78}\approx0.5769[/tex]

The answer is 0,5769