Conditional Probability Statistics

[whitehorsey]

1. Assume that there is a 50% chance of hard drive damage if a power line to which a computer is connected is hit during an electrical storm. There is a 5% chance that an electrical storm will occur on any given summer day in a given area. If there is a 0.1% chance that the line will be hit during a storm, what is the probability that the line will be hit and there will be hard drive damage during the next electrical storm in this area?



2. Bayes Theorem? P(A|B) = (P(B|A) * P(A))/ P(B)



3. I'm thinking it has something to do with Bayes Theorem...
P(hard drive damage) = 0.5
P(electrical storm) = 0.05
P(line hit) = 0.001

I started off by figuring out what is the probability of the line getting hit:
P(l|es) = (0.001 * 0.05)/ 0.05 = 0.001
but I'm not sure what I should do next and if my P(l|es) is correct.

 

[haruspex]

The circumstance is 'the next storm', and you know the probability of a hit during such a storm. The probability of a storm is irrelevant.
So you have: prob of a hit; prob of damage given a hit.

 

[HallsofIvy]

1. Assume that there is a 50% chance of hard drive damage if a power line to which a computer is connected is hit during an electrical storm. There is a 5% chance that an electrical storm will occur on any given summer day in a given area. If there is a 0.1% chance that the line will be hit during a storm, what is the probability that the line will be hit and there will be hard drive damage during the next electrical storm in this area?

Here is how I would do this problem:
Since the problem says "during the next electrical storm", the "There is a 5% chance that an electrical storm will occur on any given summer day in a given area" is irrelevant- we are given that there is a storm. Suppose there are 1000000 electrical storms. There is a .1% (.001) chance of a line being hit by lightning. So out of 1000000, how many lines are hit by lightning? Of those, 50%= .5 will result in hard drives damaged. So of those 1000000 storms, how many drives are damaged? What proportion is that?

2. Bayes Theorem? P(A|B) = (P(B|A) * P(A))/ P(B)
3. I'm thinking it has something to do with Bayes Theorem...
P(hard drive damage) = 0.5
P(electrical storm) = 0.05
P(line hit) = 0.001

I started off by figuring out what is the probability of the line getting hit:
P(l|es) = (0.001 * 0.05)/ 0.05 = 0.001
but I'm not sure what I should do next and if my P(l|es) is correct.

 

[whitehorsey]

Thank You!