Question 4 $1 / 1 p$ A famous hypnotist performs in Meany Hall before a crowd of 350 students and 180 non-students. The hypnotist knows from previous experience that one-half of the students and two-thirds of the non-students are hypnotizable. What is the probability that a randomly chosen person from the audience will be hypnotizable or will be a non-student?

Step 1 ：Let's denote the total number of people in the audience as \(total\_people\), the number of hypnotizable students as \(hypnotizable\_students\), the number of hypnotizable non-students as \(hypnotizable\_non\_students\), and the number of non-students as \(non\_students\).

Step 2 ：We can calculate these values as follows: \(total\_people = 350 + 180 = 530\), \(hypnotizable\_students = 350 \times \frac{1}{2} = 175\), \(hypnotizable\_non\_students = 180 \times \frac{2}{3} = 120\), and \(non\_students = 180\).

Step 3 ：The total number of hypnotizable people, denoted as \(total\_hypnotizable\), is the sum of \(hypnotizable\_students\) and \(hypnotizable\_non\_students\), which is \(175 + 120 = 295\).

Step 4 ：We can calculate the probability of a person being hypnotizable, denoted as \(P\_A\), by dividing \(total\_hypnotizable\) by \(total\_people\), which is \(\frac{295}{530} \approx 0.56\).

Step 5 ：We can calculate the probability of a person being a non-student, denoted as \(P\_B\), by dividing \(non\_students\) by \(total\_people\), which is \(\frac{180}{530} \approx 0.34\).

Step 6 ：The probability of a person being both hypnotizable and a non-student, denoted as \(P\_A\_and\_B\), is the probability of a non-student being hypnotizable, which is \(\frac{120}{530} \approx 0.23\).

Step 7 ：Finally, we can calculate the probability of a person being hypnotizable or a non-student, denoted as \(P\_A\_or\_B\), using the formula \(P\_A + P\_B - P\_A\_and\_B\), which is \(0.56 + 0.34 - 0.23 = 0.67\).

Step 8 ：Final Answer: The probability that a randomly chosen person from the audience will be hypnotizable or will be a non-student is approximately \(\boxed{0.67}\).