## Question

2. Sixty percent of employees in a certain engineering firm have an engineering degree, thirty percent have a business degree, and twenty percent have both, engineering and business degree. If an employee in the engineering firm is randomly chosen, what is the probability that he or she has an engineering degree or has a business degree, but not both.

3. The probability that a surface to air missile hits its intended target is 0.6. If a target is spotted on the radar and 3 missiles are launched simultaneously,

a. what distribution would you use to determine the probability that the target is destroyed?

b. Find the probability that the target is destroyed?

4. A manufacturing process produces items in a continuous manner. 10 manufactured items are placed in a box. If 3 of 10 are defective and if 5 items are randomly selected from the box and tested and not replaced,

a. what distribution would you use to determine the probability that exactly 2 items are defective?

b. Find the probability that exactly 2 items are defective?

5. The average number of new cases of a newly discovered disease is 0.5 per day, if we have 2 drug treatments for the disease left (one treatment will cure one infected individual).

a. what distribution would you use to determine what is the probability that our treatment will last for at least 3 more days?

b. What is the probability that our treatment will last for at least 3 more days?

6. Items are randomly sampled from a production line and tested for quality. They are classified as “good” or “bad”. We can assume that the production quality of each item is independent. The quality control manager claims that the probability that a “bad” item is produced is 0.05. In a sequential sample of 7 items, the 7th item selected was the 3rd defect.

a. What distribution would you use to calculate the probability that, the 7th item selected was the 3rd defect?

b. What is the probability that the 7th item selected was the 3rd defect?

7. In designing an elicitation procedure for the number of accidents at a plant, the analyst inserts the following instruction

It has been noted at similar plants that the occurrence of serious accidents is relatively low, on the order of 0.02 per month, however, due to the rash of recent minor accidents reported in the newspaper, the probability of minor accidents may be much higher. What is your estimate of the number of minor accidents per month?

a. What expert biases might this type of instruction invoke?

b. If the elicitation is from current plant safety supervisors, what additional bias should you be aware of?

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