Manufacturing process produces 40 computer circuit boards, including 7 that are defective. The quality control?

manufacturing process produces 40 computer circuit boards, including 7 that are defective. The quality control department selects 10 at random for testing and will shut down the plant for trouble shooting if 1 or more in the sample are found defective. What is the probability that the plant will be shut down?


Manufacturing process produces 40 computer circuit boards, including 7 that are defective. The quality control?
This is a probability-based question. Basically in order for the plant to not shut down, the quality control department must select a functional computer circuit board on each of 10 attempts. I assume the computer circuit board that is being tested is not restored back to the pool of boards for selection so that you are not retesting the same boards. Therefore, after making the first selection, the pool actually decreases by 1. After calculating this probability, you can subtract it from 1 to get the actual probability that the plant will be shut down.





The calculation is as follows:


(33/40) x (32/39) x (31/38) x (30/37) x (29/36) x (28/35) x (27/34) x (26/33) x (25/32) x (24/31) = 0.109


1 - 0.109 = 0.891





So the probability that the plant will be shut down is 89%.Manufacturing process produces 40 computer circuit boards, including 7 that are defective. The quality control?
I had this exact same problem im my txtbook. Was it somethign something probability for scientists and engineers?



100%





In actual practice failure rate of about 5% is really good, 10% is acceptable.