MATHEMATICS HIGH SCHOOL

A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 3% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?

Answers

Answer 1
Answer:

Answer:

0.8594

Step-by-step explanation:

Let a denote the event of forgetting to shut off machine and b be the event of being defective.

-A foreman forgets to shut off machine 55% of the time.

-If he forgets, 15% of molds are defective.

-If he does not, 3% of molds are defective.

#The probability that he forgot to shut off the machine is calculated as:

P(a \ and \ b)=0.55* 0.15\n\n=0.0825\n\n

P(a and ~b)=0.55(1-0.15)=0.4675

P(~a and b) = (1-0.55)*0.03=0.0135

P(~a and ~b) = (1-0.55)*(1-0.03)=0.4365

#Conditional probability is defined as:

P(a|b)=(P(a \ and\ b))/(P(a))\n\n=(P(a \ and \ b))/([(P(a \ and \ b)+P(\~a \ and \ b))\n\n\n=(0.0825)/(0.0825+0.0135)\n\n\n=0.8594

Hence,  the probability that the foreman forgot to shut off the machine the previous night is 0.8594

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Answers

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Step-by-step explanation:

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Answers

1 year = 365 days
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Answers

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Answers

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Answer:

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Answers

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