Electric circuit boards are rated excellent, acceptable, orunacceptable. Suppose

Question

Electric circuit boards are rated excellent, acceptable, orunacceptable. Suppose that 30% of boards are excellent, 60%are acceptable, and 10% are unacceptable. Further, supposethat 10% of excellent boards fail, 20% of acceptable boards fail,and 100% of unacceptable boards fail (unacceptable boards arediscarded without being used).

a) What is the probability that a board is rated excellent andfails?
b) What is the probability that a board fails?
c) Given that a board fails, what is the probability that it wasrated excellent?

Explanation / Answer

30% of boards were excellent of them 10% of them have failedso .1*.3= .03 or 3% b) What is the probability that a board fails? 30% of boards were excellent 10% of them have failed so .1*.3=.03 or 3% 60% of boards were acceptable 20% of them have failed so .2*.6=.12 or 12% 10% of boards were unacceptable 100% of them have failed so.1*1= .1 or 10% 3+12+10 = 25% chance a board will fail c)Given that a board fails, what is the probability that it was ratedexcellent? Ifthere was 100 boards 25 would fail and 3 of the failed would beexcellent so 3/25 or 12% of failed boards wereexcellent

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