Consider an industrial process in the textile industry in which strips of a particular type of cloth are being produced. these strips are 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 the 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?

If a strip is selected randomly from the process, and a quick measurement identifies it as failing the length test, the probability that a texture is defective is 8%

Represent the event that a strip fails the texture test with T, and the event that a strip fails the length test with L

So, we have:

[tex]\mathbf{P(T) = 5\%}[/tex]

[tex]\mathbf{P(L) = 10\%}[/tex]

[tex]\mathbf{P(T\ and\ L) = 0.8\%}[/tex]

The probability that a strip is defective given that it fails the length test is represented as: P(T|L)

So, we have:

[tex]\mathbf{P(T|L) = \frac{P(T\ and\ L)}{P(L)}}[/tex]

Substitute known values

[tex]\mathbf{P(T|L) = \frac{0.8\%}{10\%}}[/tex]

Cancel out the percentages

[tex]\mathbf{P(T|L) = \frac{0.8}{10}}[/tex]

Divide

[tex]\mathbf{P(T|L) = 0.08}[/tex]

Express as percentage

[tex]\mathbf{P(T|L) = 8\%}[/tex]

Hence, the probability that a texture is defective is 8%