Suppose a certain city has 50 licensed restaurants, of which 15 currently have at least one serious health code violation and the other 35 have no serious violations. There are five inspectors, each of whom will inspect one restaurant during the coming week. The name of each restaurant is written on a different slip of paper, and after the slips are thoroughly mixed, each inspector in turn draws one of the slips without replacement. Label the ith trial as a success if the ith restaurant selected has no serious violations. A certain state has 500,000 licensed drivers, of whom 400,000 are insured. A sample of 10 drivers is chosen without replacement. The ith trial is labeled S if the ith driver chosen is insured. Although this situation would seem identical to the example above, the important difference is that the size of the population being sampled is very large relative to the sample size. In this case P(S on 2 | S on 1) = 399,999 499,999 = (rounded to five decimal places) and P(S on 10 | S on first 9) = 399,991 499,991 = (rounded to six decimal places) ≈ 0.80000 These calculations suggest that although the trials are not exactly independent, the conditional probabilities differ so slightly from one another that for practical purposes the trials can be regarded as with constant P(S) = (rounded to one decimal place). Thus, to a very good approximation, the experiment is with n = 10 and p = 0.8.
Suppose a certain city has 50 licensed restaurants, of which 15 currently have at least one serious health code violation and the other 35 have no serious violations. There are five inspectors, each of whom will inspect one restaurant during the coming week. The name of each restaurant is written on a different slip of paper, and after the slips are thoroughly mixed, each inspector in turn draws one of the slips without replacement. Label the ith trial as a success if the ith restaurant selected has no serious violations.
A certain state has 500,000 licensed drivers, of whom 400,000 are insured. A sample of 10 drivers is chosen without replacement. The ith trial is labeled S if the ith driver chosen is insured. Although this situation would seem identical to the example above, the important difference is that the size of the population being sampled is very large relative to the sample size. In this case
| 399,999 |
| 499,999 |
and
| 399,991 |
| 499,991 |
These calculations suggest that although the trials are not exactly independent, the conditional probabilities differ so slightly from one another that for practical purposes the trials can be regarded as with constant P(S) = (rounded to one decimal place). Thus, to a very good approximation, the experiment is with n = 10 and p = 0.8.
Probability = favorable/Total
S(denote success)
F(denote fail )
(1) :
Total = 50 (15 currently have at least one serious health code violation and 35 have no serious violation)
Inspector draws one of slip without replacement.
Success (Si) = i th restorant has no serious violation.
(2) :
Total = 500000
Insured = 400000
Sample of 10 drivers are choosen without replacement.
Success (Si) = i th driver choosen is insured
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