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Problem 1: Estimate the area of the colored region (in orange) by Monte-Carlo simulation with 5000 replications given the distances shown in the figure below.
Problem 2: Quality assurance procedure of a manufacturer consists of 2 consecutive tests. Probability that a part passes the first quality test is 0.8. This probability remains the same for the second test if the part passed the first test. If a part fails the first test, then probability that it passes the next test is lower and estimated to be around 0.6. If a part passes the other, then it is reworked. Finally, if a part fails both tests then it is considered a lost cause and is scrapped. Using the U[0, 1] numbers given below:
Parts
1
2
3
4
5
6
7
8
9
10
Test 1
0.32
0.68
0.23
0.45
0.39
0.10
0.40
0.95
0.99
0.67
Test 2
0.66
0.86
0.78
0.63
0.16
0.91
0.80
0.61
0.64
a. Simulate the quality assurance procedure for 10 parts. Use your simulation results to estimate the probability that a part is used in production, reworked or scrapped.
b. Estimate the probability that a part that is send to rework had failed the first test.
c. Compute the true probabilities that a part is used in production, reworked or scrapped.
d. Compute the true probability that a part had passed the first test given that it is sent for rework.
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