in a class of 147 students, 95 are taking math, 73 are taking science, and 52 are taking both math and science. if one student is picked at random, what is the probability of choosing a student who is not taking math or science?

Step-by-step explanation: Given that here are 147 students in a class, out of which 95 students are taking math and 73 are taking science. The number of students who are taking both math and science is 52.

We are to find the probability of choosing a student who is not taking math or science, if a students is picked up at random.

Let 'M' and 'S' represents the set of students who are taking math and science respectively.

Then, according to the given information, we can write

[tex]n(M)=95,~~n(S)=52,\\\\n(M\cap S)=\textup{no. of students who are taking both math and science}=52.[/tex]

Therefore, the number of students who are taking math or science is given by

[tex]n(M\cup S)=n(M)+n(S)-n(M\cap S)=95+73-52=168-52=116.[/tex]

Hence, the number of students who are not taking math or science

= 147 - 116 = 31.

So, the probability of selecting a students who is not taking math or science will be

[tex]P=\dfrac{\textup{no. of students who are not taking math or science}}{\textup{total number of students}}\\\\\Rightarrow P=\dfrac{31}{147}=0.2108=0.2108\times 100\%=21.08\%.[/tex]

Thus, the probability is 21.08%.