Question

(2 pts) Amid students in a certain Capstone group, 60% have taken ​Linear Algebra ​ , 50% have taken ​Calculus 3 ​ , and 30% have taken both. What portion of the students… a. If someone took ​Calculus 3 ​ , what is the probability that he/she took ​Linear Algebra ​ too? b. If someone took ​Linear Algebra ​ , what is the probability that he/she took ​Calculus 3 ​ too?

Answer 1

a. 0.6

b. 0.5

Explanation:

Let A be the event that student takes algebra and C be the event that student takes Calculus 3.

P(A)=0.60

P(C)=0.5

P(A and C)=0.30

a.

We have to find P(A/C).

P(A/C)=P(A and C)/P(C)=0.3/0.5=0.6

Thus, if someone took ​Calculus 3, the probability that he/she took ​Linear Algebra ​ too is 0.6 or 60%

b.

We have to find P(C/A)

P(C/A)=P(A and C)/P(A)=0.3/0.6=0.5

Thus, if someone took ​Linear Algebra, ​the probability that he/she took ​Calculus 3 ​ too is 0.5 or 50%