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 was in the 37-46 are group

\(\displaystyle{R}={370}\)

Let B represent the event of selecting a student who received a "B" in the course. Some of these students are of 37-46 age group, so

\(\displaystyle{B}={420}\)

\(\displaystyle{P}{\left({R}{\quad\text{or}\quad}{B}\right)}={\frac{{{n}{\left({R}\right)}+{n}{\left({B}\right)}}}{{{n}{\left({S}\right)}}}}={\frac{{{370}+{420}}}{{{1940}}}}={\frac{{{790}}}{{{1940}}}}={\frac{{{79}}}{{{194}}}}\)

Therefore, probability that the selected student was in the 37-46 are group or received a "B" in the course is \(\displaystyle{\frac{{{79}}}{{{194}}}}\).

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 was in the 37-46 are group

\(\displaystyle{R}={370}\)

Let B represent the event of selecting a student who received a "B" in the course. Some of these students are of 37-46 age group, so

\(\displaystyle{B}={420}\)

\(\displaystyle{P}{\left({R}{\quad\text{or}\quad}{B}\right)}={\frac{{{n}{\left({R}\right)}+{n}{\left({B}\right)}}}{{{n}{\left({S}\right)}}}}={\frac{{{370}+{420}}}{{{1940}}}}={\frac{{{790}}}{{{1940}}}}={\frac{{{79}}}{{{194}}}}\)

Therefore, probability that the selected student was in the 37-46 are group or received a "B" in the course is \(\displaystyle{\frac{{{79}}}{{{194}}}}\).