The U.S. Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are 8 authors in total. What is the probability that none of the 8 names of these authors were among the 10 most common? (Assume that authors' names are independent and follow the same probability distribution as the names of all residents.) Give your answer to three decimal places. probability:
The U.S. Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are 8 authors in total.
What is the
Binomial distribution :
Binomial distribution describes the possible number of events occurs in fixed number of trials.
Properties of Binomial distribution:
- Each trial can have only two outcomes which can be considered success or failure.
- There must be fixed number of trials.
- Outcomes of each trails must be independent of each other.
- The probability of success must be same in each trail
The probability of obtaining x successes in the n independent trails of Binomial experiments is given by,
, x = 0,1, 2 , 3 …………n
Where, p is the probability of success.
n is number of times trial repeated.
X is random variable represents a count of the number of success in n trails.
----> combination formula.
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