Question

a physics class has 40 students. of these, 11 students are physics majors and a total of 14 students are minoring in math, including 3 students that are both majoring in physics and minoring in math. find the probability that a randomly selected student is minoring in math or a physics major. the probability that a randomly selected student is minoring in math or a physics major is \boxed{}. (round to three decimal places as needed.)

Explanation:

Step1: Define Events

Let \( A \) be the event that a student is a physics major, and \( B \) be the event that a student is minoring in math. We know:

• Total students \( n = 40 \)
• \( n(A) = 11 \) (physics majors)
• \( n(B) = 14 \) (math minors)
• \( n(A \cap B) = 3 \) (both physics major and math minor)

Step2: Apply Inclusion - Exclusion Principle

The formula for \( P(A \cup B) \) is \( P(A \cup B)=\frac{n(A)+n(B)-n(A \cap B)}{n} \)
Substitute the values: \( n(A)+n(B)-n(A \cap B)=11 + 14-3=22 \)

Step3: Calculate Probability

\( P(A \cup B)=\frac{22}{40}=0.55 \)

Answer:

\( 0.55 \)