Suppose a manager is testing electrical components for defects

As an economist for ABC Plastics, your boss has asked you to respond to some questions she has regarding the company’s main product, tablet cases
July 9, 2020
Describe the various levels of penalties that someone can face for breaking the following laws including the Computer Fraud and Abuse Act of 1986 and
July 9, 2020

Suppose a manager is testing electrical components for defects

Assuming a standard deck of 52 playing cards (for questions 1 to 4), calculate the probability of each event described below:

1)
         Draw one card that is red.

           

2) 
        Draw one card that is a queen and a heart.

3)         
Draw one card that is either a queen or a heart.

4) 
        Draw one card. What is the probability that it is a king, given that it is a club?

5) 
        Suppose a manager is testing electrical components for defects. The expected defect rate is 10 percent. The test, however, is not a perfect indicator of defects. If the unit does have a defect, the probability of the test positively identifying the defect is 99 percent. However, the probability of the test positively indicating a defect when the component does not have a defect is 2 percent. Use Bayes’ theorem to calculate the probability that a component is defective, given a positive test.

 
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Assuming a normal die with six sides, we will define Event A: you roll the die and it’s even.  We will define Event B: you roll the die and it is less than 5.  Calculate the probabilities for the next 2 questions.

6)         
Roll the dice once.  What is the probability that Event A will occur given that Event B has already occurred?

7)
         Roll the dice once.  What is the probability that Event B will occur given that Event A has already occurred?

A manager wants to start drug testing at work, and he wants to find out how accurate the tests truly are.  Suppose a drug tests 99% accurate.  This means, the probability that the test is positive given that the person does drugs is 99%.  Likewise, the probability that the test is negative given that the person is a non drug user is 99% also.  The probably that people do drugs in the workforce is .5%. Using Bayes’ Theorem find the probabilities of the next two questions.

8)         
What is the probability that an employee is a drug user given the test is positive?

9)
         What is the probability that an employee is a drug user given that the test is negative?

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