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Exercise 3.10. (ELECTRIC CIRCUITS ARE FUN) Electric circuit boards are rated exc

ID: 3365396 • Letter: E

Question

Exercise 3.10. (ELECTRIC CIRCUITS ARE FUN) Electric circuit boards are rated excellent, acceptable, or unacceptable. Suppose that 30% of boards are excellent, 60% are acceptable, and 10% are unacceptable. Further, suppose that l 0% of excellent boards fail, 20% of acceptable boards fail, and 100% of fail (unacceptable boards are discarded without being used) (a) What is the probability a board is rated excellent and fails? unacceptable boards Fig. 3.10. Circuit board. (b) What is the probability that a board fails? (c) Given that a board fails, what is the probability that it was rated excellent?

Explanation / Answer

a) probability that a board rated excellent and fails =0.30*0.10 =0.03

b) probability that a board fails =P(excellent and fails+acceptable and fails+unacceptable and fails)

=0.3*0.1+0.6*0.2+0.1*1 =0.25

c) probability that it was rated excellent given board fails =P(excellent and board fails)/P(board fails)

=0.3*0.1/0.25=0.12