Question

A school counts the number of students taking AMDM and find 237 students taking AMDM. They alsocount the number of students taking Physics and find 214 students taking the Physics. When they comparethe two lists they find 78 student taking AMDM and Physics. What is the probability of a student takingAMDM given they are taking Physics. (Answer in decimal form rounded to the thousandth)

Answer 1

In order to solve this question, we need to use conditional probability. The formula for the probability of event A happening knowing that event B has happened, P(A | B), is:

P(A | B) = P(A ∩ B)/P(B)

where P(A ∩ B) is the probability of A and B both happening.

From the given information, and using T to represent the total number of students, we have:

P(Physics) = 214/T

P(AMDM ∩ Physics) = 78/T

Now, using that information into the formula for the conditional probability, we find:

P(AMDM | Physics) = P(AMDM ∩ Physics)/P(Physics)

P(AMDM | Physics) = (78/T) / (214/T)

= (78/T) * (T/214)

= 78/214 since T/T = 1

≅ 0.364

Therefore, the probability of a student taking AMDM given they are taking Physics is approximately 0.364.