Answer:
0.5 or 50%
Step-by-step explanation:
From Bayes' Theorem,
[tex]P(A\ |\ B)=\dfrac{P(A)\cdot P(B\ |\ A)}{P(B)}[/tex]
In a school of 1250 students, 250 are freshmen and 150 students take Spanish.
So,
[tex]P(\text{Freshmen})=\dfrac{250}{1250}=0.2[/tex]
[tex]P(\text{Spanish})=\dfrac{150}{1250}=0.12[/tex]
[tex]P(\text{Spanish}\ |\ \text{Freshmen})=30\%=0.30[/tex]
Applying Bayes' Theorem,
[tex]P(\text{Freshmen}\ |\ \text{Spanish})=\dfrac{P(\text{Freshmen})\cdot P(\text{Spanish}\ |\ \text{Freshmen})}{P(\text{Spanish})}[/tex]
[tex]=\dfrac{0.2\times 0.30}{0.12}[/tex]
[tex]=0.5[/tex]
