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 but no French.
6 take French and German but not Spanish.
24 students are taking at least two languages.

What is the probability that a student randomly selected from those taking exactly one language takes French in this semester?

Best done with a Venn diagram.

overlap three circles called S F and G
place x in the middle for S F and G
fill in the rest of the entries
e.g. the number taking only Spanish = 42 - 8 - 8 - x
= 26-x

similarly:
only German = 45 - 8 - 6 - x = 31 - x
only French = 46 - 8 - 6 - x = 32 - x

we can find x ....
26-x +8+8+6+x+32-x+31-x = 107
-2x = -4
x = 2

so those taking only French = 32-2= 30

prob of stated event = 30/107

2+2=4

Let's do 100+90+4. You are thinking now this is impossible but no you can sum this the answer of this you are thinking that is 194 so yes cause just you need to put the one of the hundred place, the nine of the tens place and the four of the ones place

27563-23421=4142

just sing ou your communities property of multiplication with different thousanda hunts and ones

To calculate the probability that a student randomly selected from those taking exactly one language takes French, we need to find the number of students taking French as their only language and divide it by the total number of students taking exactly one language.

To do this, let's break down the information provided:

- There are a total of 107 foreign language students.
- 42 students take Spanish.
- 46 students take French.
- 45 students take German.
- 8 students take Spanish and French but not German.
- 8 students take Spanish and German but no French.
- 6 students take French and German but not Spanish.
- 24 students are taking at least two languages.

To find the number of students taking French as their only language, we need to subtract the students taking multiple languages from the total number of French students. Here's how:

Total French students = 46
French students taking Spanish and French but not German = 8
French students taking French and German but not Spanish = 6

French students taking only French = Total French students - French students taking multiple languages
= 46 - (8 + 6)
= 46 - 14
= 32

So, there are 32 students taking French as their only language.

Now, to find the total number of students taking exactly one language, we need to subtract the students taking multiple languages from the total number of foreign language students. Here's how:

Total foreign language students = 107
Students taking at least two languages = 24

Students taking exactly one language = Total foreign language students - Students taking at least two languages
= 107 - 24
= 83

Therefore, there are 83 students taking exactly one language.

The probability that a student randomly selected from those taking exactly one language takes French can be calculated as:

Probability = Number of students taking French as their only language / Number of students taking exactly one language
= 32 / 83
≈ 0.3855

So, the probability is approximately 0.3855 or 38.55%.