# To calculate: The probability that the selected student was in the 27-36 are group. Given Information: A table depicting the grade distribution for a college algebra class based on age and grade.

To calculate: The probability that the selected student was in the 27-36 are group.
Given Information:
A table depicting the grade distribution for a college algebra class based on age and grade.

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Macsen Nixon
Formula used:
In a sample space, S, of equally likely, the probability of an event E is given by
$$\displaystyle{P}{\left({E}\right)}={\frac{{\nu{m}{b}{e}{r}\ {o}{f}\ {e}\le{m}{e}{n}{t}{s}\ \in\ {t}{h}{e}\ {e}{v}{e}{n}{t}}}{{\nu{m}{b}{e}{r}\ {o}{f}\ {e}\le{m}{e}{n}{t}{s}\ \in\ {t}{h}{e}\ {s}{a}\mp\le\ {s}{p}{a}{c}{e}}}}={\frac{{{n}{\left({E}\right)}}}{{{n}{\left({S}\right)}}}}$$
Calculation:
Denote the sample space as
$$\displaystyle{S}={1940}$$
Let R represent the event of selecting a student who received an "A" in the course, so
$$\displaystyle{R}={440}$$
$$\displaystyle{P}{\left({R}\right)}={\frac{{{n}{\left({R}\right)}}}{{{n}{\left({S}\right)}}}}={\frac{{{650}}}{{{1940}}}}={\frac{{{65}}}{{{194}}}}$$
Therefore, probability that the selected student was in the 27-36 age group is $$\displaystyle{\frac{{{65}}}{{{194}}}}$$.