Answer:
The theoretical probability of four students from your school being selected as contestants out of 8 possible contestants spots = [tex]\frac{14}{165}[/tex]
Step-by-step explanation:
The number of students participated = 30
Total audience = 150
By probability , to find the solution = [tex]\frac{n(E)}{n(S)}[/tex]
where n(E) is the number of favorable outcomes,
n(S) is the number of total outcomes.
n(S) is the number of ways any 8 students can by picked from the audience= [tex]\frac{8}{140}[/tex]
n(E) is the probability of picking four students from our school and five students from another school.
n(E) = [tex](\frac{4}{30}) (\frac{4}{110})[/tex] = [tex]\frac{16}{3300}[/tex]
[tex]\frac{n(E)}{n(S)}[/tex] = [tex]\frac{\frac{16}{3300}}{\frac{8}{140}}[/tex] = [tex]\frac{14}{165}[/tex]
