SOLUTION: An irs person randomly selects 3 tax returns with out replacement from 47 returns of which 5 contain errors. What is the probability that she selects none of those containing erro

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Question 1127883: An irs person randomly selects 3 tax returns with out replacement from 47 returns of which 5 contain errors. What is the probability that she selects none of those containing errors? Answer in decimal form.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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An irs person randomly selects 3 tax returns without replacement from 47 returns of which 5 contain errors.
What is the probability that she selects none of those containing errors? Answer in decimal form.
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So,  we have  47  items, in all.

Of them,  there are  5  special items.

We select  3  arbitrary items from these  47  items.

The question is:  what is the probability that we select none of those  5  special items.


Solution

    In all, we can select   =  = 16215 different triples of 47 item, taking 3 at a time.


    It is the entire space of events.


    How many triples can we select avoiding these 5 special items ? - It means that we select triples 
    from  47-5 = 42 items of the complementary set.


    The number of these "ideal" (or favorable) triples is therefore   =  = 11480.


    Therefore, the probability under the question is   = 0.708 (with 3 correct decimal places),  or  70.8%.

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.


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