math

There are a total of 152 foreign language students in a high school where they offer only Spanish, French, and German.

You are given the following details for this semester:

58 take Spanish.

71 take French.

66 take German.

9 take Spanish and French but not German.

9 take Spanish and German but not French.

15 take French and German but not Spanish.

38 students are taking at least two languages.

1. How many students take all three languages in this semester?

2. How many students take only French in this semester?

3. What is the exact probability that two students selected from this school take French? Enter your answer as a rational number:

  1. 👍 0
  2. 👎 0
  3. 👁 259
  1. Use Venn diagrams.
    Make 3 overlapping circles, and label them S, F, and G
    Place x in the intersection of all 3
    and then place the 9, 9, and 15 in their correct regions
    In the "Spanish only" part, put in 40-x
    In the "French only" part, put in 47-x
    In the "German only" part, put in 42-x

    We are told 38 are taking at least two languages, that would be the regions showing some overlap, so
    9+9+15+x = 38
    x = 5

    1. 5 take all 3
    2. 42 take only French
    3. prob = (71/152)(70/151) = 2485/11476

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    There are a total of 103 foreign language students in a high school where they offer Spanish, French, and German. There are 19 students who take at least 2 languages at once. If there are 38 Spanish students, 38 French students,

    asked by Lane on March 7, 2013
  2. Math - Probabilities

    There are a total of 116 foreign language students in a high school where they offer Spanish, French, and German. There are 22 students who take at least 2 languages at once. If there are 47 Spanish students, 45 French students,

    asked by Sarah on March 11, 2013
  3. Math

    There are a total of 103 foreign language students in a high school where they offer Spanish, French, and German. There are 29 students who take at least 2 languages at once. If there are 40 Spanish students, 42 French students,

    asked by Jun on May 29, 2016
  4. Math

    There are a total of 103 foreign language students in a high school where they offer Spanish, French, and German. There are 19 students who take at least 2 languages at once. If there are 38 Spanish students, 38 French students,

    asked by Lane on March 8, 2013
  5. math

    There are a total of 107 foreign language students in a high school where they offer only Spanish, French, and German. 42 take Spanish. 46 take French. 45 take German. 8 take Spanish and French but not German. 8 take Spanish and

    asked by Christy on December 15, 2010
  6. English

    Can you help me check this letter, please? 1) teach German in a high school with an emphasis on applied sciences. Our students are between 13 and 18 years old and are all motivated to learn. 2) They will therefore go to university

    asked by Henry2 on September 30, 2011
  7. MATH SETS AND COUNTING

    There are a total of 103 foreign language students in a high school where they offer only Spanish, French, and German. You are given the following details for this semester: 44 take Spanish. 44 take French. 42 take German. 7 take

    asked by LEILA on October 4, 2010
  8. English

    I'm posting you the sentences again. Thank you for your corrections. 1) I teach German in a high school with an emphasis on applied sciences. Our students are between 13 and 18 years old and are all motivated to learn. 2) They

    asked by Henry2 on September 30, 2011
  9. English

    I forgot to include these other questions. I'm going to arrange them according to their topic (school, sports activities, travelling (?), clothes (?), student exchange programm, family, food). Do you think the topics are all

    asked by Mike on March 14, 2011
  10. math

    can you help ; i need to write and solve for each situation. check the solution. school: between 7:30am and 8:00am the number of students in a school increased by 73. there were 152 students in the school at 8:00 am. How many

    asked by marko on September 19, 2012

More Similar Questions