Answer:
To complete the two-way table, we will have that
[tex]\begin{gathered} Total\text{ algebra=10} \\ n(P)+n(not\text{ in physics\rparen=19} \\ 4+n(not\text{ in physics\rparen=19} \\ n(not\text{ in physics\rparen=19-4} \\ n(not\text{ in physics\rparen=15} \end{gathered}[/tex][tex]\begin{gathered} total\text{ physics=12} \\ n(P)+n(not\text{ in physics\rparen=12} \\ 4+n(not\text{ in physics\rparen=12} \\ n(not\text{ in physics\rparen=12-4} \\ n(not\text{ in physics\rparen=8} \end{gathered}[/tex][tex]\begin{gathered} The\text{ total=30} \\ n(algebra)+n(not\text{ algebra\rparen=30} \\ 19+n(not\text{ algebra\rparen=30} \\ n(not\text{ algebra\rparen=30-19} \\ n(not\text{ algebra\rparen=11} \end{gathered}[/tex][tex]\begin{gathered} Total=30 \\ n(physics\text{ total\rparen+n\lparen not physics total\rparen=30} \\ 12+n\left(notphysicstotal\right)=30 \\ n\left(notphysicstotal\right)=30-12 \\ n\left(notphysicstotal\right)=18 \end{gathered}[/tex][tex]\begin{gathered} n(not\text{ inphysicstotal\rparen=18} \\ n(notinphyicsA)+n(not\text{ in physics,not in algebra\rparen=18} \\ 15+n(not\text{ in physics,not in algebra=18} \\ n(not\text{ in physics,not in algebra=18-15} \\ +n(not\text{ in physics,not in algebra=3} \end{gathered}[/tex]
Hence,
The complete table is given below as
Therefore,
The students who enrolled in either Algebra or Physics will be
[tex]\begin{gathered} =15+8 \\ =23 \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow23[/tex]
The SECOND OPTION is the right answer
