Question

The probability that a student at your school takes Drivers Education and Spanish is 87/1000. The probability that a student takes Spanish is 68/100. What is the probability that a student takes Drivers Ed given that the Student is taking Spanish?

Answer 1

Answer: The probability is P = 0.128

Explanation:

The data we have is:

The probability of a student to take drivers education and Spanish is 87/1000.

The probability that a student takes Spanish is 68/100.

Now, remember that if for event 1 we have the probability p1, and for event 2 we have the probability p2, the probability of both events happening is:

P = p1*p2

This is the case for the student that takes the two classes, but when we assume that the student takes Spanish, we can remove the probability of that event (because we are already looking at the 68/100 of the cases where the student selected Spanish)

So given that a student is tanking Spanish, the probability of him to take drivers ed is:

(Probability of both classes)/(probability of tanking Spanish)

P = (87/1000)*(100/68) = 0.128

Answer 2

let
x---------> The probability that a student takes Spanish
y-------> the probability that a student takes Drivers Education given that the Student is taking Spanish
z-------> The probability that a student at school takes Drivers Education and Spanish

we know that
z=x*y------> solve for y
y=z/x
z=87/1000
x=68/100
substitute
y=(87/1000)/(68/100)-----------> y=87/680

the answer is
87/680