Question

Cars in a parking lot:SUVHonda68RedHow many SUV's are in the parking lot? 20How many red Hondas are in the parking lot? 20хHow many of the red cars in the parking lot are not SUV? 15How many cars are in the parking lot? 34Question Help: Video

Answer 1

The given data are

`\begin{gathered} \upsilon\Rightarrow universal\text{ set=450} \\ n(M)=\text{ marist=205} \\ n(B)=\text{ 260} \\ n(\text{NCs)}=240 \\ n(M\cap NCs)=95 \\ n(NC\text{s }\cap\text{ B)=115} \\ n(\text{ B}\cap M)=105 \\ n(B\cap M\cap NCs)=50 \\ \text{let n(B}\cup M\cup NCs)=x \end{gathered}`
`\begin{gathered} n(M\cap NCS\cap B^(\prime))=95-50=45 \\ n(\text{NCS}\cap B\cap M^(\prime))=115-50=65 \\ n(B\cap M\cap NCS^(\prime))=105-50=55 \\ \text{Therefore,} \\ n(M\cap B^(\prime)\cap NCS^(\prime))=205-(45+55+50)=205-150=55 \\ n(B\cap M^(\prime)\cap NCS^(\prime))=260-(55+50+65)=260-170=90 \\ n(\text{NCS}\cap B^(\prime)\cap M^(\prime))=240-(45+50+65)=240-160=80 \end{gathered}`

Therefore, to calculate x we will have that

`\begin{gathered} 45+65+55+55+90+80+50+x=450 \\ 440+x=450 \\ x=450-440 \\ x=10 \end{gathered}`

1) The number of students that attended only the FSU -BUTLER GAME

`n(B\cap NCS^(\prime)\cap M^(\prime))=90`

2) The number of students that did not attend Marist, butler, or North Carolina state Carolina game is,

`n(B\cup M\cup NCS)^(\prime)=10`

3) Number that attended at least two of the games are

`\begin{gathered} n(B\cap M\cap NCS^(\prime))+n(B\cap NCS\cap M^(\prime))+n(M\cap NCS\cap B^(\prime))+n(B\cap MNC) \\ 55+65+45+50=215 \end{gathered}`

4) The number of students that attended the marist and butler games but not the North Carolina games is

`n(M\cap B\cap NCS^(\prime))=55`

5) The number of students that attended the North Carolina state or butler games is

`\begin{gathered} n(\text{NCS }\cap B^(\prime)\cap M^(\prime))+n(B\cap NCS^(\prime)\cap M^(\prime))+n(B\cap NCS\cap M^(\prime)) \\ =80+90+65=235 \end{gathered}`