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(52835)   (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   =  = 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   =  = 10.

It is the number of favorable elements.



Now the probability under the question is  P =  =  =  = 0.08333... = 8.333%.     ANSWER

Solved.

-----------------

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.


/\/\/\/\/\/\/\/

Solution 2.

The probability that the first applicant randomly selected by the manager has a college degree is   = ;


same about the second applicant is  ;


same about the third applicant is  .


The product of these probabilities is   =  = 0.08333... = 8.333%,


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



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