Question

PROBLEM 1 Assume that 0.5% of all semiconductor parts produced in a manufacturing process break within one year. The parts can be tested with a very reliable but not perfect screening procedure: • 2.5% of the parts that break within one year pass the test 1% of the parts that do not break within one year do not pass the test A part just failed this test. What is the probability that this part will break within one year?

please use Bayes theorem and show work. thank you :)

Answer 1

TOPIC:Application of the Bayes' theorem.

= Problem - 14 Define the following events as B: The part breaks within one year ; The part passed the test. and, P: i Given that, P (B) = 0.005 (in decimals) 2) P (B4) = 1- P(B) -0.995 Also we have, P PC Passed rotest the Breahs within n = 0.025 I one year , = P (P1B) = 0.025. 22P (PC/B) = 1-P (P(B) = 0.975. Again, do not pass! Do not break ( the test within one year = 0.ol. =) P (PC IBC) = 0.01

we need = P Breaks within one year the the part failed) test. = P (B(PC). Bayes' theorem P (B). P (PB) P(B). P(P44B) +P(BS). P(p*B9 0.005 X 0.975 0.005 . xo. 975 to 995 x 0.01 - To. 3288 To na (Rounded to I jour decimals)