# Conditional probability

1. Nov 14, 2007

1. The problem statement, all variables and given/known data

The probability of a monitor not working is 0.005, the probability of a cpu faulty is 0.002, the probability of a keyboard damaged is 0.0025, what is the probability of the computer switching on? If you are then told that the conditional probability of the monitor not working given that the keyboard has been damaged is 0.05, how does this affect the answer?

2. Relevant equations
probability of monitor not working = 0.005
probability of cpu faulty = 0.002
probability of keyboard damaged = 0.0025

3. The attempt at a solution
For the first part is was solved ok with a venn diagram removing from 1 the summed up individual probabilities and the intersect probabilities giving 0.009472475, however for the second part I attempted adding P(M|K) to to each occurence of p(K) in(where P(k) is probability of the keyboard being damaged) the general equation obtained from the venn diagram, but my answer was off the mark of 0.0936025

2. Nov 15, 2007

### HallsofIvy

Staff Emeritus
What exactly is meant by "the computer switching on"? That none of those malfunctions happens? 0.009472475 is the probability of at least one of those malfunctions happening and I have trouble reconciling that with "the computer switching on"!

Last edited: Nov 15, 2007
3. Nov 15, 2007

My apologies maybe I should have stressed 0.009472 is the probability that the computer will be operational i.e will switch on i.e 1 - ((probability that the keyboard is damaged) + (probability that the cpu is faulty) + ( probability that the monitor will fail) - (p of monitor failing and keyboard failing) - p(keyboard damaged and cpu faulty) - p(cpu faulty and monitor damaged) - p(monitor fails and keyboard is damaged and cpu is faulty))

= 0.009472

4. Nov 15, 2007

### HallsofIvy

Staff Emeritus
Are you serious? The probability of each of those failures is less than 1% yet you say that the probability that the computer will work at all is less than 1%?
What you have calculated is the probability that at least one of those things has gone wrong and so (I guess) that the computer will NOT turn on. That can, by the way, be done more simply: The probability that the monitor will not work is 0.005 so the probability the monitor WILL work is 0.995. The probability that the cpu will not work is 0.002 so the probability it WILL work is 0.998. The probability that the keyboard will not work is 0.0025 so the probability that it WILL work is 0.9975. That probability that everything will work is the product of those: (0.995)(0.998)(0.9975)= .990527 so the probability of at least one malfunction (the computer will NOT work) is 1- .990527= .009472, as you have.