-aux07.Venn diagram -about 120 students in a school

[karush]

(a) since $n(U)=120$ and the intersections showing $8,7$ and $4$ added is $19$ then $\displaystyle\frac{19}{120}$ is the probability of studying exactly $2$ languages

(b) since $n(J)=35$ then subtracting $8,5,7$ would be $15$ so $\displaystyle\frac{15}{120}=\frac{1}{8}$ would be probability of studying only Japanese

(c) $\displaystyle\frac{n(C)\ \cup\ n(J)\cup \ n(S)}{n(U)}=
\frac{19}{30}$

 

[Evgeny.Makarov]

(a) and (b) are correct. As for (c), you need to subtract your answer from 1 because the question asks for the probability that the student does not study any of these languages. The expression $n(C)\cup n(J)$ is a type error because $n(C)$ and $n(J)$ are numbers, while $\cup$ acts on sets. I agree that $n(C\cup J\cup S)=19\cdot4=76$, but it is strange that you did not explain this more difficult part while you explained the easier ones.

 

[karush]

(a) and (b) are correct. As for (c), you need to subtract your answer from 1 because the question asks for the probability that the student does not study any of these languages. The expression $n(C)\cup n(J)$ is a type error because $n(C)$ and $n(J)$ are numbers, while $\cup$ acts on sets. I agree that $n(C\cup J\cup S)=19\cdot4=76$, but it is strange that you did not explain this more difficult part while you explained the easier ones.

I probably misunderstood the notation. so $\frac{19}{30}$ is the probability that a student will study a language. and $\frac{11}{30}$ is the probability that a student does not study a language.

so saying $14\cup 16$ is improper it has to a $A\cup B$ etc

 

[Evgeny.Makarov]

I probably misunderstood the notation. so $\frac{19}{30}$ is the probability that a student will study a language. and $\frac{11}{30}$ is the probability that a student does not study a language.

Yes.

so saying $14\cup 16$ is improper it has to a $A\cup B$ etc

Yes.

 

[CellCoree]

would be the probability of studying at least one language

I would like to clarify that the Venn diagram and the calculations provided are based on assumptions and may not accurately represent the actual situation. The data used to create the Venn diagram and calculate the probabilities should be carefully collected and analyzed to ensure accuracy. Additionally, it is important to note that the probabilities calculated are based on the assumption that all students have an equal chance of studying each language, which may not be the case in reality. Further research and data analysis would be needed to fully understand the language preferences and choices of the students in this school.