zeion
Sep28-11, 07:52 PM
1. The problem statement, all variables and given/known data
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 any one 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.
2. Relevant equations
3. 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) ?
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 any one 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.
2. Relevant equations
3. 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) ?