SOLUTION: A) Ten people apply for a job as assistant manager of a restaurant. Five have completed college and five have not. If the manager selects 3 applicants at random, find the probabili

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Question 1136905: A) Ten people apply for a job as assistant manager of a restaurant. Five have completed college and five have not. If the manager selects 3 applicants at random, find the probability that all 3 are college graduates.
B) The Statistical Bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. If a random sample of 8000 births is taken, find the mean, variance, and standard deviation of the number of births that would result in twins.
Answer by ikleyn(52815) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I will solve the problem (A) only.


Solution 1. 

In how many ways the manager can select 3 applicants from 10 persons ?

In  C%5B10%5D%5E3 = %2810%2A9%2A8%29%2F%281%2A2%2A3%29 = 120 ways.

It is the number of combinations of 10 items taken 3 at a time.

At the same time, it is the number of elements in the entire space of events.



How many triples exist consisting of applicants with the college degree ?

They all are selected from the sub-set of 5 applicants having college degree.

Hence, the number of such triples is  C%5B5%5D%5E3 = %285%2A4%29%2F%281%2A2%29 = 10.

It is the number of favorable elements.



Now the probability under the question is  P = favorable%2Fall = 10%2F120 = 1%2F12 = 0.08333... = 8.333%.     ANSWER

Solved.

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On Combinations,  see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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Solution 2. 

The probability that the first applicant randomly selected by the manager has a college degree is  5%2F10 = 1%2F2;


same about the second applicant is  4%2F9;


same about the third applicant is  3%2F8.


The product of these probabilities is  %281%2F2%29%2A%284%2F9%29%2A%283%2F8%29 = 12%2F144 = 0.08333... = 8.333%,


and you get the same answer as in the Solution 1.



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