- #1
lavoisier
- 177
- 24
Hi everyone, a colleague at work asked me a question this morning, which I answered with the caveat that I wasn't really sure. I would like to hear your opinion, please.
His question was the following
I have two different methods A and B to obtain a given desired outcome, and it's known that the probability of success of A is 90%, and the one of B is 80%.
If I apply both methods, what is the probability that at least one of them succeeds?
My initial answer was:
P(A or B) = 1 - P(not(A) AND not(B)) = 1 - P(not(A))*P(not(B)) = 1 -0.1*0.2 = 98%
Then I thought, what if the events where A and B succeed (or fail) are not independent?
In that case I couldn't say: P(not(A) AND not(B)) = P(not(A))*P(not(B))
But instead:
P(A or B) = P(A) + P(B) - P(A AND B)
where:
P(A AND B) = P(A) * P(B|A) = P(B) * P(A|B)
I sent another email to my colleague with this observation. But I don't know if this is correct, either. And if it is, I don't know how we could determine the conditional probability, given that (he said) the two methods would be applied independently.
What do you think?
Have we got enough information to answer this question?
If not, what else do we need to know?
Thanks!
L
His question was the following
I have two different methods A and B to obtain a given desired outcome, and it's known that the probability of success of A is 90%, and the one of B is 80%.
If I apply both methods, what is the probability that at least one of them succeeds?
My initial answer was:
P(A or B) = 1 - P(not(A) AND not(B)) = 1 - P(not(A))*P(not(B)) = 1 -0.1*0.2 = 98%
Then I thought, what if the events where A and B succeed (or fail) are not independent?
In that case I couldn't say: P(not(A) AND not(B)) = P(not(A))*P(not(B))
But instead:
P(A or B) = P(A) + P(B) - P(A AND B)
where:
P(A AND B) = P(A) * P(B|A) = P(B) * P(A|B)
I sent another email to my colleague with this observation. But I don't know if this is correct, either. And if it is, I don't know how we could determine the conditional probability, given that (he said) the two methods would be applied independently.
What do you think?
Have we got enough information to answer this question?
If not, what else do we need to know?
Thanks!
L