Lesson Students studying foreign languages
Algebra
->
Probability-and-statistics
-> Lesson Students studying foreign languages
Log On
Algebra: Probability and statistics
Section
Solvers
Solvers
Lessons
Lessons
Answers archive
Answers
Source code of 'Students studying foreign languages'
This Lesson (Students studying foreign languages)
was created by by
ikleyn(52756)
:
View Source
,
Show
About ikleyn
:
<H2>Students studying foreign languages</H2> <H3>Problem 1</H3>A survey of 100 students asked if they studied a foreign language. The result showed: Spanish, 28; German, 30; French, 42; Spanish and German, 8; Spanish and French,10; German and French 5; all three languages,3. What is the probability that a randomly selected student studied no foreign language? <B>Solution</B> <pre> Let S be the subset of the 100 students studied Spanish, and let |S| be the cardinality of the subset S. We are given |S| = 28. Let G be the subset of the 100 students studied German, and let |G| be the cardinality of the subset G. We are given |G| = 30. Let F be the subset of the 100 students studied French, and let |F| be the cardinality of the subset F. We are given |F| = 42. Let SG be the subset of the 100 students studied Spanish and German. It is the intersection of the sets S and G. And let |SG| be the cardinality of the subset SG. We are given |SG| = 8. Let SF be the subset of the 100 students studied Spanish and French. It is the intersection of the sets S and F. And let |SF| be the cardinality of the subset SF. We are given |SF| = 10. Let GF be the subset of the 100 students studied German and French. It is the intersection of the sets G and F. And let |GF| be the cardinality of the subset GF. We are given |GF| = 5. Finally, let SGF be the subset of the 100 students studied Spanish, German and French. It is the intersection of the sets S, G and F. And let |SGF| be the cardinality of the subset SGF. We are given |GF| = 3. Now, the number of students among of 100 surveyed who studied at least one of these three languages was N = |S| + |G| +|F| - |SG| - |SF| - |GF| + |SGF| = 28 + 30 + 42 - 8 - 10 - 5 + 3 = 80. Thus 80 students of 100 learned at least one language. The rest of 100, 100-80 = 20, do not study these languages. Therefore, the probability that a randomly selected student studied no foreign language is {{{20/100}}} = {{{1/5}}}. <U>Answer</U>. The probability that a randomly selected student studied no foreign language is {{{1/5}}}. </pre> The formula we used is well known in the elementary set theory. Its proof is very straightforward and simple. See, for example, the lesson - <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. My other lessons on <B>Probability</B> in this site are <TABLE> <TR> <TD> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Simple-and-simplest-probability-problems.lesson>Simple and simplest probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability.lesson>Solving probability problems using complementary probability</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-True-False-test.lesson>A True/False test</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-multiple-choice-answers-test.lesson>A multiple choice answers test</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Coinciding-birthdays.lesson>Coinciding birthdays</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-shipment-containing-fair-and-defective-alarm-clocks-.lesson>A shipment containing fair and defective alarm clocks</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/People-in-a-room-write-down-integer-numbers-at-random.lesson>People in a room write down integer numbers at random</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-drawer-contains-a-mixture-of-socks.lesson>A drawer contains a mixture of socks</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-for-a-computer-to-be-damaged-by-viruses.lesson>Probability for a computer to be damaged by viruses</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Using-sample-space-to-solve-Probability-problems.lesson>Using sample space to solve Probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-probability-problems-from-the-archive.lesson>Typical probability problems from the archive</A> </TD> <TD> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Geometric-probability-problems.lesson>Geometric probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Advanced-probability-problems-from-the-archive.lesson>Advanced probability problems from the archive</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Challenging-probability-problems.lesson>Challenging probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Selected-probability-problems-from-the-archive.lesson>Selected probability problems from the archive</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Experimental-probability-problems.lesson>Experimental probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson>Rolling a pair of fair dice</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Ten-pairs-of-shoes-are-kept-in-a-rack.lesson>Ten pairs of shoes are kept in a rack</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-diplomat-and-spies.lesson>A diplomat and spies</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-operations-on-sets-help-solving-Probability-problems.lesson>Elementary operations on sets help solving Probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Independent-and-mutually-exclusive-events.lesson>Independent and mutually exclusive events</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Unusual-probability-problems.lesson>Unusual probability problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-problem-for-the-Day-of-April-1.lesson>Probability problem for the Day of April, 1</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/OVERVIEW-of-lessons-on-Probability.lesson>OVERVIEW of lessons on Probability</A> </TD> </TR> </TABLE> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-II.
