# To calculate: The probability that a student chosen randomly from the class is not going to college if the number of students in a high school graduating class is 128, out of which 52 are on the honor roll, and out of these, 48 are going to college. The number of students who are not on the honor roll is 76,out of these 56 are going to college.

Question
Upper level algebra
To calculate: The probability that a student chosen randomly from the class is not going to college if the number of students in a high school graduating class is 128, out of which 52 are on the honor roll, and out of these, 48 are going to college. The number of students who are not on the honor roll is 76,out of these 56 are going to college.

2020-10-19
Calculation:
Consider the total number of students in the class to be 128.
Therefore, $$\displaystyle{n}{\left({S}\right)}={128}$$.
Compute the number of students who are on the honor roll and not going to college.
$$\displaystyle{56}-{48}={4}$$
Compute the number of students who are not on the honor roll and not going to college.
$$\displaystyle{76}-{56}={20}$$
Compute the total number of students not going to college.
$$\displaystyle{n}{\left({E}\right)}={4}+{20}={24}$$
Compute the probability of event E by dividing the number of outcomes of an event by the number of outcomes of sample space.
$$\displaystyle{P}{\left({E}\right)}={\frac{{{n}{\left({E}\right)}}}{{{n}{\left({S}\right)}}}}$$
$$\displaystyle={\frac{{{24}}}{{{128}}}}$$
$$\displaystyle={\frac{{{3}}}{{{16}}}}$$
Therefore, the probability that a student is not going to college is $$\displaystyle{\frac{{{3}}}{{{16}}}}$$.

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To calculate: The probability that a student chosen randomly from the class is not going to college and on the honor roll if the number of students in a high school graduating class is 128, out of which 52 are on the honor roll, and out of these, 48 are going to college. The number of students who are not on the honor roll is 76, out of these 56 are going to college.
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