In a school, 14% of students take drama and computer classes, and 67% take drama class. What is the probability that a student takes computer class given that the student takes drama class?

Question

Abigail Allen · Accepted Answer

The probability is #=0.21#

The probability of taking drama is #P(D)=0.67#

The probability of taking computer and drama is #P(DnnD)=0.14#

The probability of taking computer given he has taken drama is

#P(C|D)=(P(DnnD))/(P(D))=0.14/0.67=0.21#

Genesis Allen · Answer

undefined To find the probability that a student takes computer class given that the student takes drama class, we use conditional probability.

Let $D$ represent the event that a student takes drama class, and let $C$ represent the event that a student takes computer class.

Given that 14% of students take both drama and computer classes, and 67% take drama class, the probability of a student taking computer class given that the student takes drama class is:

$$ P(C|D) = \frac{P(C \cap D)}{P(D)} $$

We know that $P(C \cap D) = 0.14$ and $P(D) = 0.67$.

So,

$$ P(C|D) = \frac{0.14}{0.67} $$

$$ P(C|D) ≈ 0.208 $$

Therefore, the probability that a student takes computer class given that the student takes drama class is approximately 0.208.