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

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1)
         Draw one card that is red.

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

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

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

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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.

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

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

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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.

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

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

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