Question

a physics class has 50 students. of these, 18 students are physics majors and a total of 16 students are minoring in math, including 7 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
(round to three decimal places as needed.)

Explanation:

Step1: Use the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a student is minoring in math and \(B\) be the event that a student is a physics major.
The total number of students \(n = 50\).
The number of students minoring in math \(n(A)=16\), so \(P(A)=\frac{n(A)}{n}=\frac{16}{50}\).
The number of students who are physics majors \(n(B) = 18\), so \(P(B)=\frac{n(B)}{n}=\frac{18}{50}\).
The number of students who are both minoring in math and physics majors \(n(A\cap B)=7\), so \(P(A\cap B)=\frac{n(A\cap B)}{n}=\frac{7}{50}\).

Step2: Calculate \(P(A\cup B)\)

Substitute the values into the formula:

$$
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$$

Answer:

\(0.54\)