Multiplication Law for Several Events

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
  customers 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.
• Prwindshield was not washedJanet 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