math
posted by Amber
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 93 students in the school. There are 35 in the Spanish class, 31 in the French class, and 22 in the German class. There are 12 students that in both Spanish and French, 6 are in both Spanish and German, and 8 are in both French and German. In addition, there are 2 students taking all 3 classes.
If one student is chosen randomly, what is the probability that he or she is not in any of these classes?
If two students are chosen randomly, what is the probability that at least one of them is taking a language class?
Show work or an explanation please!

Scott
draw a Venn diagram of three intersecting circles enclosed in a box
label the circles S, F, and G
S/F/G  2 ... these are in all the two way intersections
S/F  10 + (2)
S/G  4 + (2)
F/G  6 + (2)
S  19 + (2) + (10) + (4)
F  13 + (2) + (10) + (6)
G  10 + (2) + (4) + (6)
language students
... 19 + 13 + 10 + 6 + 4 + 10 + 2 = 64
nonlanguage ... 93  64
"at least one" means that both cannot be nonlanguage
Respond to this Question
Similar Questions

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 Spanish … 
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 … 
math
107 total foreign language students 42 take spanish 46 take french 45 take german 8 take spanish & french but not german 6 take french & german but not spanish 8 take spanish & german but not french 24 students are taking at least … 
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 German … 
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, and … 
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, and … 
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, and … 
math
Bridget surveyed some students at her school about their favorite classes. Of the students surveyed, 3 said Spanish was their favorite class, while 9 of the students had other favorite classes. If Bridget surveys 8 more students, how … 
Math
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 107 students in the school. There are 42 in the Spanish class, 32 in the French class, and … 
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, and …