Question

In a school of 1250 students, 250 are freshmen and 150 students take Spanish. The probability that a student takes Spanish given that he/she is a freshman is 30%. What is the probability that a randomly selected student is a freshman given that he/she takes Spanish?

Answer 1

Answer:

0.5 or 50%

Step-by-step explanation:

From Bayes' Theorem,

$P(A\ |\ B)=\dfrac{P(A)\cdot P(B\ |\ A)}{P(B)}$

In a school of 1250 students, 250 are freshmen and 150 students take Spanish.

So,

$P(\text{Freshmen})=\dfrac{250}{1250}=0.2$

$P(\text{Spanish})=\dfrac{150}{1250}=0.12$

$P(\text{Spanish}\ |\ \text{Freshmen})=30\%=0.30$

Applying Bayes' Theorem,

$P(\text{Freshmen}\ |\ \text{Spanish})=\dfrac{P(\text{Freshmen})\cdot P(\text{Spanish}\ |\ \text{Freshmen})}{P(\text{Spanish})}$

$=\dfrac{0.2\times 0.30}{0.12}$

$=0.5$

Answer 2

The answer is 45/150 which is simplified to 3/10