Given that a student takes Japanese, what is the likelihood that he or she is in the anime club?
The likelihood that a student who takes Japanese is in the anime club is approximately 10.67%.
Understanding Conditional Probability:
Conditional probability is the likelihood of an event occurring given that another event has already occurred. In this case, we are interested in finding the probability that a student is in the anime club, given that the student takes Japanese.
When dealing with conditional probability, we use the formula:
P(A|B) = P(A and B) / P(B)
Where:
- P(A|B) is the probability of event A given event B
- P(A and B) is the probability of events A and B occurring together
- P(B) is the probability of event B occurring
In the context of the Fairview High School data, the probability of a student taking Japanese and being in the anime club is 0.16, and the probability of a student taking Japanese is 0.15.
Therefore, to find the likelihood that a student who takes Japanese is in the anime club, we divide the probability of taking Japanese and being in the anime club by the probability of taking Japanese:
P(In anime club|Takes Japanese) = P(Takes Japanese and In anime club) / P(Takes Japanese) = 0.16 / 0.15 = 0.1067
So, the likelihood that a student who takes Japanese is in the anime club is approximately 10.67%.
For further understanding of conditional probability, you can explore more resources on the topic. It is an important concept in probability theory and has various real-world applications in data analysis, statistics, and decision-making.