My question: How does the microwave not working affect the probability of the light not working in the kitchen! Unless you assume a power outage why should they both be dependent events ??? Confused. Took a screenshot of question image shack: http://yfrog.com/mrmbsix2p Solution It is because you misunderstood the notion of being dependent/independent. These concepts are really specifically internal to the subject of probability and in that view more technical than intuitive. So it has nothing to do with power outage or anything non-probabilistic reasoning. Here is my explanation as to how they are (probabilistic) dependent: We consider a population consisting of electric devices of various kinds, lights, radios, microwaves etc. Let us say we have n devices all together. Let b denote the number of devices not working. Then we have: P(light in the kitchen not working) = b/n Then we are told that the microwave doesn\'t work. Since we know this we have n-1 devices left in our population and b-1 of these are broken. Thus P(light in the kitchen not working given that the microwave is not working) = (b-1)/(n-1) And b/n only equals (b-1)/(n-1) if b=n because then b/n = (b-1)/(n-1) <=> (multiplying by n and (n-1)) b(n-1) = (b-1)n <=> (expanding parentheses) bn-b = bn-n <=> (adding b+n-bn to both sides) n = b This means that if to begin with not all of the devices are broken the probability of the light in the kitchen being broken is changed by the knowledge that we have removed one device, the microwave, from the population. Thus the probability of the light being broken depends on this knowledge and hence is a dependent event..

1. My question: How does the microwave not working affect the probability of the light not
working in the kitchen! Unless you assume a power outage why should they both be dependent
events ??? Confused.
Took a screenshot of question image shack:
http://yfrog.com/mrmbsix2p
Solution
It is because you misunderstood the notion of being dependent/independent. These
concepts are really specifically internal to the subject of probability and in that view more
technical than intuitive. So it has nothing to do with power outage or anything non-probabilistic
reasoning. Here is my explanation as to how they are (probabilistic) dependent: We consider a
population consisting of electric devices of various kinds, lights, radios, microwaves etc. Let us
say we have n devices all together. Let b denote the number of devices not working. Then we
have: P(light in the kitchen not working) = b/n Then we are told that the microwave doesn't
work. Since we know this we have n-1 devices left in our population and b-1 of these are broken.
Thus P(light in the kitchen not working given that the microwave is not working) = (b-1)/(n-1)
And b/n only equals (b-1)/(n-1) if b=n because then b/n = (b-1)/(n-1) <=> (multiplying by n and
(n-1)) b(n-1) = (b-1)n <=> (expanding parentheses) bn-b = bn-n <=> (adding b+n-bn to both
sides) n = b This means that if to begin with not all of the devices are broken the probability of
the light in the kitchen being broken is changed by the knowledge that we have removed one
device, the microwave, from the population. Thus the probability of the light being broken
depends on this knowledge and hence is a dependent event.