Answer to Question #267235 in Statistics and Probability for usama

Question

Question 5

The concept of conditional probability has countless uses in both industrial and biomedical applications. Consider an industrial process in the textile industry in which strips of a particular type of cloth are being produced. These strips can be defective in two ways, length and nature of texture. For the case of the latter, the process of identification is very complicated. It is known from historical information on the process that 10% of strips fail the length test, 5% fail the texture test, and only 0.8% fail both tests. If a strip is selected randomly from the process and a quick measurement identifies it as failing the length test, what is the probability that it is texture defective?

Answer 1

conditional probability of B, given A:

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

we have:

the probability that it is texture defective is P(B|A),

the probability offailing the length test is P(A),

the probability that fail both tests

then:

the probability that it is texture defective if it is failing the length test:

$P(B|A)=\frac{0.008}{0.1}=0.08=8\%$