2. A quality control officer was checking the quality of a product on the manufacturing line. For an individual product, the probability that it is defective is 0.05. We may treat the individual...

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Extracted text: 2. A quality control officer was checking the quality of a product on the manufacturing line. For an individual product, the probability that it is defective is 0.05. We may treat the individual products as independent Bernoulli trials. Suppose the inspector stays on the line until the third defective product is observed. What is the probability of observing ten non-defective products before the third defective product was observed? 3. The director of human resources on a university campus selects two employees for a certain job from a group of six employees. This group consists of one female and five males. What is the probability that the female is selected for one of the jobs? 4. In an assembly line production using industrial robots, a particular component can be installed on the main product in 90 seconds if holes have been drilled in the component and 12 minutes if the holes have to be re-drilled on the component. Twenty of the components are in stock and it is assumed that two will have improperly drilled holes. Five of the components are selected at random from the twenty for installation for the next five robots in line. What is the probability that all five components will fit properly?