Question

Discrete math:

A company uses computer vision software for quality inspection of its products. Over all products, 1 out of 10 is defective. The software labels non-defective products to be correct in 17 out of 18 cases. Defective products are (falsely) labeled to be correct in 1 out of 5 cases. Given that a product is labeled to be correct, what is the probability that it is actually defective?

		5/64
		2/87
		0.0018
		0.078

The producer of a laboratory test for detecting a virus estimated the following table of conditional probabilities for the test. The test can be either true (T) or false (F) and a patient may either carry the virus (+) or not carry the virus (-). In addition, we know that the prevalence for a virus infection (probability to have the virus given no prior knowledge) is p(+) = 0.002.

p( test | patient )	patient +	patient -
test T	0.93	0.81
test F	0.07	0.19
	1.00	1.00

What is the probability to carry the virus if the test is positive?

		0.0389
		0.0313
		0.0427
		0.0023

Answer 1

1)

probability that it is actually defective given labeled correct

=P(defective and labeled correct)/P( labeled correct )

=(1/10)*(1/5)/((1/10)*(1/5)+(9/10)*(17/18))

=2/87

2)

probability to carry the virus if the test is positive =(0.002*0.93)/(0.002*0.93+(1-0.002)*0.81)=0.0023