probability

• Feb 9th 2007, 05:55 PM
probability
Hi,
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)?

For the first question,
I did this:
P(device correct)=(.97)(.94)

The second I dont know what to do.

Please can someone help me ?
• Feb 9th 2007, 11:16 PM
CaptainBlack
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

RonL

(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)
• Feb 9th 2007, 11:56 PM
CaptainBlack
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)?

2- If there are N welds tested, of these 0.03N are defective, and of these
0.94(0.03N) give a positive signal.

There are 0.97N non defectives and of these 0.05(0.97N) give a positive
signal.

So the probability that the weld is not defective given that the device gives
a positive signal is the ratio of the number of non-defectives giving a positive
signal to the total number of positive signals:

0.05(0.97N)/[0.05(0.97N)+0.94(0.03N)]=0.0485/[0.0485+0.0282]=0.632

(scarry Eh?)

RonL
• Feb 10th 2007, 05:25 PM