# Suppose a manager is testing electrical components for defects

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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:

**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.

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?