My book has the question
"One design for a system requires the installation of two identical components. The system will work if at least one of the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9, and if the components function independently, which design has the greater probability of functioning?"
I know p*p for and and p+p for or, so for the two component system with only one needing to function you have together 0.9 chance for one plus 0.9 probability for the other total chance for it to work, so 1.8.
For the 4 component system I initially started to do 0.9*0.9+0.9*0.9, but then realized that would only be/cover two combos, such as (if have components a b c d) a&b or c&d, not something like a&c b&d.
So would I have to do that for every combo like:
a 0.9 * b 0.9 + c 0.9 * d 0.9 + a 0.9 * c 0.9 + b 0.9 * d 0.9 + a 0.9 * d 0.9 + c 0.9 * b 0.9
Or is there some simpler trick to this I"m missing?
Edit: Will wait.. you shouldn't have p above 1 so... all that's off?