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

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

Answer 2

0.5 or 50%

Explanation:

From Bayes' Theorem,

`P(A\ |\ B)=(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})=(250)/(1250)=0.2`

`P(\text{Spanish})=(150)/(1250)=0.12`

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

Applying Bayes' Theorem,

`P(\text{Freshmen}\ |\ \text{Spanish})=\frac{P(\text{Freshmen})\cdot P(\text{Spanish}\ |\ \text{Freshmen})}{P(\text{Spanish})}`

`=(0.2* 0.30)/(0.12)`

`=0.5`