This may be a silly question but I am confused on how to proceed. I have a family A of items: A1, A2, A3, A4 and A5 which were being randomly stress tested for failure. I computed the probability of failure of family A (consisting of A1 through A5) as the number of items that failed during the stress testing period divided by the total population of the family.
Now, how can I compute the probability that two items will fail together assuming both dependent and independent failures?
I am thinking that if they are independent then the estimate would be:
$P(A1) * P(A2) * (1-P(A3)) * (1-P(A4)) * (1-P(A5))$ $=P(A)^2 * (1-P(A))^3$
I am not sure if this is close to what I want though. However, I am also curious to know how to solve this if the events are dependent. Any suggestions?