Question

a physics class has 50 students. of these, 14 students are physics majors and a total of 18 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
(round to three decimal places as needed.)

Explanation:

Define the given values and events

Using the Probability Axioms knowledge point
Let \(S\) be the sample space of all students in the physics class.
Let \(P\) be the event that a randomly selected student is a physics major.
Let \(M\) be the event that a randomly selected student is minoring in math.

We are given:

• Total number of students: \(n(S) = 50\)
• Number of physics majors: \(n(P) = 14\)
• Number of students minoring in math: \(n(M) = 18\)
• Number of students who are both: \(n(P \cap M) = 3\)

Calculate individual and joint probabilities

Using the Probability Axioms knowledge point

$$
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$$

Apply the addition rule for non-mutually exclusive events

Using the Mutually Exclusive Events knowledge point
Since the events \(P\) and \(M\) share common outcomes, they are not mutually exclusive. We apply the general addition rule:

$$ P(P \cup M) = P(P) + P(M) - P(P \cap M) $$

Substituting the calculated probabilities:

$$ P(P \cup M) = 0.28 + 0.36 - 0.06 = 0.58 $$

Format the final result

Using the Probability Axioms knowledge point
The calculated probability is \(0.58\).
Rounding to three decimal places as requested yields \(0.580\).

Answer:

A physics class has 50 students. Of these, 14 students are physics majors and a total of 18 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 <blank>0.58</blank>
(Round to three decimal places as needed.)