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Answer:
0.4460 = 44.60% probability that none of the 8 surnames of these authors were among the 10 most common
Step-by-step explanation:
For each surname, there are only two possible outcomes. Either they are among the 10 most common, or they are not. Each author is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
These names account for 9.6% of all U.S. residents.
This means that
8 authors in total.
This means that
What is the probability that none of the 8 surnames of these authors were among the 10 most common
This is . So
0.4460 = 44.60% probability that none of the 8 surnames of these authors were among the 10 most common