Question 1049719
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In a class of 100 people, 25 own fords, 20 own dodges, 13 own toyotas, 10 own both fords and dodges, 8 own fords and toyotas, 5 own dodges and toyotas, and 4 own all three. If a person selected at random from the class, what is the probability he or she does not own any of these vehicles? Use a venn diagram.
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Similar problem was solved in

<A HREF=https://www.algebra.com/statistics/Binomial-probability/Binomial-probability.faq.question.1048656.html>https://www.algebra.com/statistics/Binomial-probability/Binomial-probability.faq.question.1048656.html</A>


https://www.algebra.com/statistics/Binomial-probability/Binomial-probability.faq.question.1048656.html


Apply the same logic. 


The numbers are 


100 - [25 + 20 + 13 - (10 + 8 + 5) + 4] = 61.


So, the number of people in the class who does not own any of these vehicles is 61.


Therefore, the answer to the question is {{{61/100}}}.


The formula we used is well known in the elementary set theory.

Its proof is very straightforward and simple.

See, for example, the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook in the topic "Miscellaneous word problems" of the section "Word problems".