Answer:
[tex]P(Foreign\ Language\ n\ Sport) = \frac{7}{25}[/tex]
Step-by-step explanation:
Given
See attachment for Venn diagram
Required
Determine [tex]P(Foreign\ Language\ n\ Sport)[/tex]
First, we calculate the population of the set.
This is calculated as:
[tex]Total = Sport + Foreign\ Language + None + Both[/tex]
This gives
[tex]Total = 23 + 10 + 3+14[/tex]
[tex]Total = 50[/tex]
So, the required probability is:
[tex]P(Foreign\ Language\ n\ Sport) = \frac{n(Foreign\ Language\ n\ Sport)}{Total}[/tex]
[tex]P(Foreign\ Language\ n\ Sport) = \frac{14}{50}[/tex]
14 represents the intersection between Foreign and Sport i.e. n(Foreign n Sport)
So, we have:
[tex]P(Foreign\ Language\ n\ Sport) = \frac{7}{25}[/tex]