At a particular factory, refrigerators inspectors on an assembly line notice that a randomly selected refrigerator will have too much enamel with probability 0.2, too little enamel with probability 0.25, uneven application with probability 0.33, and no defects with probability 0.43. Note that it is not possible for the same refrigerator to have both too much and too little enamel. Draw the Venn diagram (but do not complete it) before answering the following questions: (a) What is the probability that a randomly selected refrigerator has a paint defect (i.e. either too much enamel, too little enamel, or uneven application)? (b) What is the probability of a paint defect from an improper amount of paint (i.e. too much or too little enamel)? (c) What is the probability of a paint defect resulting from uneven application but not from an improper amount of paint?

Question

At a particular factory, refrigerators inspectors on an assembly line notice that a randomly selected refrigerator will have too much enamel with probability 0.2, too little enamel with probability 0.25, uneven application with probability 0.33, and no defects with probability 0.43. Note that it is not possible for the same refrigerator to have both too much and too little enamel. Draw the Venn diagram (but do not complete it) before answering the following questions:  (a) What is the probability that a randomly selected refrigerator has a paint defect (i.e. either too much enamel, too little enamel, or uneven application)?  (b) What is the probability of a paint defect from an improper amount of paint (i.e. too much or too little enamel)?  (c) What is the probability of a paint defect resulting from uneven application but not from an improper amount of paint?

Symbee · Accepted Answer

Step 1   As per the given data,   Randomly selected refrigerator will have too much enamel with probability 0.2,   too little enamel with probability 0.25,   uneven application with probability 0.33,   and no defects with probability 0.43.    Step 2   (a) The probability that a randomly selected refrigerator has a paint defect (i.e. either too much enamel, too little enamel, or uneven application) :   P(paint defect) = 1 - P(No defect)  =1−0.43  =0.57  Step 3   (b) The probability of a paint defect from an improper amount of paint (i.e. too much or too little enamel):   P(improper amount) = [P(too much enamel)+P(too little enamel)]   =(0.2+0.25)   =0.45  Step 4   (c) The probability of a paint defect resulting from uneven application but not from an improper amount of paint:   = (probability of too much enamel + probability of too little enamel + probability of uneven application )-probability of paint defect    =(0.2+0.25+0.33)−0.57   =0.21

At a particular factory, refrigerators inspectors on an assembly line

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