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A university class has had $9$ undergraduate students enroll so far, as well as $9$ other students. What is the experimental probability that the next student to enroll will be an undergraduate student? Simplify your answer and write it as a fraction or whole number. $\newline$ $P(\text{undergraduate}) = \_\_\_$

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Experimental probability

Full solution

Q. A university class has had

9

undergraduate students enroll so far, as well as

9

other students. What is the experimental probability that the next student to enroll will be an undergraduate student? Simplify your answer and write it as a fraction or whole number.

\newline

P(\text{undergraduate}) = \_\_\_

Define Experimental Probability: To determine the experimental probability of an event, we need to know the number of times the event has occurred and the total number of trials. However, in this case, we are not given any past data about enrollments, so we cannot calculate an experimental probability based on past outcomes. Instead, we can only provide a theoretical probability assuming that each student has an equal chance of being an undergraduate or not.
Calculate Total Enrollment: Since there are $9$ undergraduate students and $9$ other students, there are a total of $9 + 9 = 18$ students enrolled so far. If we assume that the likelihood of the next student being an undergraduate is the same as being a non-undergraduate, then the theoretical probability of the next student being an undergraduate is the number of undergraduate spots available out of the total number of spots, which is $9$ out of $18$ .
Simplify Fraction: To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is $9$ . So, $\frac{9}{18}$ simplifies to $\frac{1}{2}$ .
Determine Theoretical Probability: Therefore, the theoretical probability that the next student to enroll will be an undergraduate student is $\frac{1}{2}$ .

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