Answer: There are 14 students not taking any foreign languages.
Step-by-step explanation: Take the total number of students and subtract it by the number of students who are taking each class. So you would get 19 for French, 12 for Spanish, and 7 for both. Then you would add those numbers up and get a total of 38. You would then do the same except subtract each total of students by 30 to find how many of the 30 are not taking each class or both. You would then get 11 for French, 18 for Spanish, and 23 for both. Add those numbers up and get 52. Then you would subtract 38 from 52 thus giving the final answer 14.
The number of students that are not taking any foreign language is 6 and P(F∪S)' = [tex]\frac{1}{5}[/tex] OR 1/5
The Venn diagram that illustrates the scenario is given in the attachment below.
x represent the number of students that are not taking any foreign language.
To determine how many students are not taking any foreign language, we will determine the value of x.
From the diagram, we can write that
F∪S + (F∪S)' = ξ
ξ represent the universal set
In the diagram,
F∪S = 12 + 7 + 5 = 24
(F∪S)' = x
and
ξ = 30
∴ 24 + x = 30
Subtract 24 from both sides
24 - 24 + x = 30 - 24
∴ x = 6
Now for P(FunionS)', that is P(F∪S)'
P(F∪S)' = n(F∪S)' / nξ
From above (F∪S)' = x
∴ n(F∪S)' = 6
Then,
P(F∪S)' = [tex]\frac{6}{30}[/tex]
∴ P(F∪S)' = [tex]\frac{1}{5}[/tex] OR 1/5
Hence, the number of students that are not taking any foreign language is 6 and P(F∪S)' = [tex]\frac{1}{5}[/tex] OR 1/5
Learn more here: https://brainly.com/question/18251610
