Question

An school is offering 3 language classes: one in spanish, one in french, and one in tagalog. the classes are open to any of the 100 students in the school. there are 28 students in the spanish class, 26 students in the french class, and 16 in the tagalog class. there are 12 students who are in both spanish and french, 4 who are in both spanish and tagalog, and 6 who are in both french and tagalog. in addition there are 2 students taking all 3 classes. (a) if a student is chosen randomly, what is the probability that he or she is not in any of the language classes

Answer 1

100-students
28-spanish
12-both spanish and french⇒     28-12-2-4=10 only spanish
 2-in all classes                                              
4 - spanish and tagalog

16 -tagalog
4- spanish and tagalog   
2 - all classes
6- french and tagalog    ⇒ 16-6-2-4=4 only tagalog

26-french
12-french and spanish
2-all classes
6-french and tagalog       ⇒ 26-12-2-6= 6 only french


the students who are in language classes are:
10+6+4+2+12+6+4=44
100-44=56 are not in language classes
P=56/100=0,56