# Conditional Probability Statistics

• whitehorsey
In summary, the probability of the line being hit and hard drive damage occurring during the next electrical storm is 0.0005 or 0.05%. This can be calculated using Bayes Theorem and taking into account the given probabilities of a line being hit during a storm and the likelihood of damage occurring if a line is hit.
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.

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.

whitehorsey said:
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.

Thank You!

## 1. What is conditional probability in statistics?

Conditional probability in statistics is a measure of the likelihood of an event occurring, given that another event has already occurred. It is expressed as P(A|B), which reads as "the probability of A given B". This means that we are interested in the probability of event A happening, assuming that event B has already occurred.

## 2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of events A and B by the probability of event B. Mathematically, it can be written as P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) represents the probability of events A and B occurring together.

## 3. What is the difference between conditional and unconditional probability?

Unconditional probability, also known as marginal probability, is the probability of an event occurring without taking into account any other events. On the other hand, conditional probability takes into consideration the occurrence of another related event. In other words, unconditional probability is calculated from the entire sample space, while conditional probability is calculated from a subset of the sample space.

## 4. How is conditional probability used in real life?

Conditional probability is used in many real-life situations, such as in medical diagnosis, weather forecasting, and financial risk analysis. For example, a doctor might use conditional probability to determine the probability of a patient having a certain disease, given their test results and medical history.

## 5. What is the relationship between conditional probability and independence?

If two events A and B are independent, then the conditional probability of A given B is equal to the unconditional probability of A. This means that the occurrence of event B does not affect the likelihood of event A happening. However, if two events are not independent, then the conditional probability of A given B will be different from the unconditional probability of A.

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