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Understanding Probability and Multiplication Law in Statistical Sampling

Learn about the General Multiplication Law applied to several events and its significance in solving complex problems, along with Conditional Probability examples involving a gas station's attendants. Discover how probability calculations are crucial in sampling results, with insights on independent sample observations and the intricacies of sampling methods.

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Understanding Probability and Multiplication Law in Statistical Sampling

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  1. Multiplication Law for Several Events General multiplication law is extended to several components

  2. The general multiplication rules are useful in solving many problems in which the ultimate outcome of an experiment depends on the outcomes of various intermediate stages.

  3. Conditional Probability The four attendants of a gasoline service station are supposed to wash the windshield of each customer’s car. Janet, who services 20% of all cars, fails to wash the windshield one time in 20 Tom, who services 60% of all cars, fails to wash the windshield one time in 10 Georgia, who services 15% of all cars, fails to wash the windshield one time in 10 Peter, who services 5% of all cars, fails to wash the windshield one time in 20.

  4. Conditional Probability If a customer later complained that her windshield was not washed, what is the probability that her car was serviced by Janet?

  5. Solution All these are mutually exclusive events. Pr[windshield was not washed|Janet serviced the car] =

  6. Probability and Sampling • Probability is especially important in summarizing potential sampling results. Because multiple observations are usually involved in statistical evaluations, the probability calculations can be complicated. Probability trees can be helpful in organizing these computations.

  7. Problem from book. • Example on page 176 (text book)

  8. Independent Sample Observation • Sampling without replacement: When inspected sample units are set aside. • Sampling

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