Question

A worker-operated machine produces a defective item with probability 0.06 if the worker follows the machine's operating instructions exactly, and with probability 0.09 if he does not. If the worker follows the instructions 90% of the time, what proportion of all items produced by the machine will be defective?

Answer 1

Answer: Our required probability is 6.3%.

Step-by-step explanation:

Since we have given that

Probability that worker operated machine produces a defective item if follow the instruction exactly = 0.06

Probability that worker produces defective item if he does not follows the machine's operating instructions exactly = 0.09

Probability that the worker follows the instruction = 90% = 0.9

Let A be the event that worker follow the instructions.

Let B be the event that machine produce defective items.

So, P(A) = 0.9, P(A') = 0.1

P(B|A) = 0.06 , P(B|A') = 0.09

So, Probability that all items produced by the machine will be defective is given by

$P(A).P(B|A)+P(A')P(B|A')\\\\=0.9\times 0.06+0.1\times 0.09\\\\=0.063\\\\=6.3\%$

Hence, our required probability is 6.3%.