Question

a physics class has 40 students. of these, 14 students are physics majors and a total of 17 students are minoring in math, including 2 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 \(n = 40\).
The number of students minoring in math \(n(A)=17\), the number of physics - majors \(n(B) = 14\), and the number of students who are both \(n(A\cap B)=2\).
Then \(P(A)=\frac{n(A)}{n}=\frac{17}{40}\), \(P(B)=\frac{n(B)}{n}=\frac{14}{40}\), and \(P(A\cap B)=\frac{n(A\cap B)}{n}=\frac{2}{40}\).

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

Substitute the values into the formula:

$$
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$$

Step3: Convert to decimal

\(\frac{29}{40}=0.725\)

Answer:

\(0.725\)