Question

A school has 100 students. 40 take English, 30 take Art. 12 take both.What is the probability that a student takes English or Art?What is the probability that a student takes English and Art?What is the probability that a student does not take English?

Answer 1

`\begin{gathered} E\colon\text{ Student take English} \\ A\colon\text{ Student take Art} \\ B\colon\text{ Student take both} \\ \\ \text{Total students:100} \\ \#E\colon40 \\ \#A\colon30 \\ \#B\colon12 \\ There\text{ are 18 students that doesn't take E and neither A} \\ \end{gathered}`

What is the probability that a student takes English or Art?:

`P(E\text{ or A)}=\frac{\#E+\#A+B}{\text{Total}}=(40+30+12)/(100)=(82)/(100)=0.82`

The probability that a student takes Ensglish or art is 82% (0.82)

What is the probability that a student takes English and Art?

`P(E\text{ and A)}=(\#B)/(Total)=(12)/(100)=0.12`

The probability that a student takes English and Art is 12% (0.12)

What is the probability that a student does not take English?

`\begin{gathered} P(\text{not E)}=1-P(E) \\ \\ P(E)=\frac{\#E+\#B}{\text{Total}}=(40+12)/(100)=(52)/(100)=0.52 \\ \\ P(\text{not E)}=1-0.52=0.48 \end{gathered}`

The probability that a student does not take English is 48% (0.48)