Conditional probability question with set theory things

In summary, the conversation discusses finding the probability of more than one independent event occurring when at least one has already occurred. The attempt at a solution involves representing the events with symbols and using conditional probability to solve for the desired probability. The specific steps and equations used are also mentioned. However, there is no response or reply to the question posed in the conversation.
  • #1
zeion
466
1

Homework Statement



Basically, I'm given the probability of 4 independent events:

P(A) = 0.04
P(B) = 0.03
P(C) = 0.02
P(D) = 0.01

If anyone of these occur, a failure will happen.
More than one can happen at the same time.

I need to find the probability that more than one of them has occurred given at least one as occurred.

Homework Equations





The Attempt at a Solution



I solved for the prob that at least one occurred:
Let F = A∪B∪C∪D
Then P(F) = P(A) + P(B) + P(C) + P(D) - P(A∩B∩C∩D) = 0.09999976

Now I have to solve for prob of 'more than one' occurred given F has occurred.
I'm stuck on this part.
How do I represent 'more than one occurred' with symbols?
Would it be E = (A∩B)∪(A∩C)∪(B∩D)∪(C∩D)?

Then P(E | F) ?
 
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  • #2
No one..?
Is my post not understandable?
 

1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is represented as P(A|B), where A is the event of interest and B is the event that has already occurred.

2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of both events (P(A∩B)) by the probability of the first event (P(B)). This can also be expressed as P(A|B) = P(A∩B) / P(B).

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

Unconditional probability, also known as marginal probability, is the likelihood of an event occurring without any prior knowledge. Conditional probability takes into account a specific condition or event that has already occurred and adjusts the probability accordingly.

4. How is set theory related to conditional probability?

Set theory is a branch of mathematics that deals with the study of collections of objects. In conditional probability, the events of interest are represented as sets, and the relationships between these sets are used to calculate the probability of the events occurring.

5. Can conditional probability be applied in real-life situations?

Yes, conditional probability can be applied in a wide range of real-life situations, such as weather forecasting, medical diagnosis, and financial risk assessment. It allows us to make more accurate predictions and decisions by taking into account the influence of previous events on the likelihood of future events.

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