Problem

A physics class has 40 students. Of these, 11 students are physics majors and 13 students are female. Of the physics majors, four are female. Find the probability that a randomly selected student is female or a physics major.

Answer

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Answer

Final Answer: The probability that a randomly selected student is either a female or a physics major is \(\boxed{0.5}\) or \(\boxed{50\%}\).

Steps

Step 1 :Given that there are 40 students in a physics class, 13 of which are female and 11 are physics majors. Among the physics majors, 4 are female.

Step 2 :We are asked to find the probability that a randomly selected student is either a female or a physics major.

Step 3 :The total number of students who are either female or physics majors can be found by adding the number of female students and the number of physics majors. However, since there are students who are both female and physics majors, they are being counted twice. To avoid this, we subtract the number of students who are both female and physics majors from the total.

Step 4 :Using the formula for the probability of an event, which is the number of ways that event can occur divided by the total number of outcomes, we can find the probability that a randomly selected student is either a female or a physics major.

Step 5 :Substituting the given values into the formula, we get \((13 + 11 - 4) / 40 = 0.5\).

Step 6 :This means that the probability that a randomly selected student is either a female or a physics major is 0.5 or 50%.

Step 7 :Final Answer: The probability that a randomly selected student is either a female or a physics major is \(\boxed{0.5}\) or \(\boxed{50\%}\).

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