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

Ok, so this can be simple math. According to calculations you can make, what would be your guess?

Answer 2

first we'd construct a venn diagram with freshmen in one circle and spanish in the other

Answer 3

"The probability that a student takes Spanish given that he/she is a freshman is 30%"

in other words, 30% of the freshman also take spanish, so 30% of 250 freshman, or 75 students, are freshman that also take spanish, so we would put that in the center of the diagram

Answer 4

now for the question actually being asked, "What is the probability that a randomly selected student is a freshman given that he/she takes Spanish?"

simply calculate

(freshman who take spanish)/(all students who take spanish)