Solve the problem.
-Of the coffee makers sold in an appliance store, 5% have either a faulty switch or a defective cord, 1.3% have a faulty switch, and 0.3% have both defects. What is the probability that a coffee maker will have a defective cord given that it has either a faulty switch or defective cord? Round to the nearest thousandth.
A)0.003
B)0.013
C)0.260
D)0.800

Question

Quizplus · Accepted Answer

To find the probability that a coffee maker has a defective cord given it has either a faulty switch or a defective cord, we use the formula for conditional probability. The probability of having a defective cord (C) given either a faulty switch (S) or a defective cord is P(C|S or C) = P(C and (S or C)) / P(S or C). We know that P(S or C) = 5%, P(S) = 1.3%, P(C and S) = 0.3%. To find P(C), we use the principle of inclusion-exclusion: P(S or C) = P(S) + P(C) - P(S and C), so 5% = 1.3% + P(C) - 0.3%, which gives P(C) = 4%. The probability of having a defective cord given either fault is P(C|S or C) = P(C) / P(S or C) = 4% / 5% = 0.8 or 80%, which rounds to 0.800.

Solve the Problem. -Of the Coffee Makers Sold in an Appliance Store, 5