Questions: Homework: Chapter 3 A physics class has 40 students. Of these, 14 students are physics majors and a total of 18 students are minoring in math, including 6 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.)

Homework: Chapter 3 A physics class has 40 students. Of these, 14 students are physics majors and a total of 18 students are minoring in math, including 6 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.)
Transcript text: Homework: Chapter 3 A physics class has 40 students. Of these, 14 students are physics majors and a total of 18 students are minoring in math, including 6 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 $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Calculating the number of individuals in either subset without double counting

To avoid double counting individuals in both subsets, we use the formula: $$A + B - AB$$ Substituting the given values, we get: $$A + B - AB = 18 + 14 - 6 = 26$$

Step 2: Calculating the probability

The probability that a randomly selected individual belongs to at least one of the two subsets is given by: $$P = \frac{A + B - AB}{N}$$ Substituting the values, we get: $$P = \frac{A + B - AB}{N} = \frac{26}{40} = 0.65$$

Final Answer:

The probability is 0.65.

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