Posted by **Amber** on Sunday, October 30, 2016 at 4:47pm.

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!

- math -
**Scott**, Sunday, October 30, 2016 at 5:28pm
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

non-language ... 93 - 64

"at least one" means that both cannot be non-language

## Answer This Question

## Related Questions

- Math - An elementary school is offering 3 language classes: one in Spanish, one ...
- math - There are a total of 107 foreign language students in a high school ...
- math - There are a total of 152 foreign language students in a high school where...
- MATH SETS AND COUNTING - There are a total of 103 foreign language students in ...
- Math - Probabilities - There are a total of 116 foreign language students in a ...
- math - Bridget surveyed some students at her school about their favorite classes...
- Math - There are a total of 103 foreign language students in a high school where...
- Math - There are a total of 103 foreign language students in a high school where...
- Math - There are a total of 103 foreign language students in a high school where...
- math - 107 total foreign language students 42 take spanish 46 take french 45 ...

More Related Questions