I have issues understanding probability.
I have this problem:
A device for checking welds in pumps is designed to signal if the weld is defective. If the weld is actually defective, the probability the device will give a signal is .94.
If the weld is actually not defective, the probability the device will give a signal is .05.
It is known that 3% of welds on pumps are defective. A weld is selected at random and checked by the device.
1- What is the probability the device will be correct?
2- Suppose the device gives a signal for the checked weld. What is the probability the weld is actually not defective (false positive)?
1- The device can be correct in two ways: the weld can be defective and the device says so, the welld could be OK and the device does not say its defective.
pr(correct)=pr(defctv)pr(declared defctv when it is) + pr(not-defctv)pr(not declared defctv when it is not)
......=0.03*0.94 + 0.97*(1-0.05)=0.9497
(I will get back to 2 if nobody else does it - but I have to go now the dog is
pestering to be taken for his walk)