A school surveyed student participation in extracurricular activities. The survey found: The drama club had 50% of students participate, the science club had 30% of students participate, both clubs had 15% of students participate. What is the probability that a student participated in the drama club, given that they attended the science club?

Rationale

The probability that a student participated in the drama club, given that they attended the science club, is 0.5.

To find this conditional probability, we apply the formula P(D|S) = P(D and S) / P(S). Here, P(D and S) is the percentage of students who participated in both clubs (15%), and P(S) is the percentage of students who participated in the science club (30%). Thus, P(D|S) = 0.15 / 0.30 = 0.5.

A (0.15) YOUR ANSWER

This choice represents the percentage of students who participated in both clubs, not the conditional probability of participating in the drama club given attendance in the science club. It does not account for the total number of students in the science club.

B (0.3) YOUR ANSWER

This option reflects the overall percentage of students participating in the science club, which is not relevant to the conditional probability being asked. It does not incorporate the relationship between the drama club and the science club.

C (0.4) YOUR ANSWER

This value is incorrect as it does not represent any calculated probability related to the clubs. It does not correspond to the participation rates given in the survey and misrepresents the relationship between the two clubs.

D (0.5) CORRECT

This is the correct calculation for the conditional probability, where the percentage of students who participated in both clubs (15%) is divided by the percentage who participated in the science club (30%), resulting in 0.5.

Conclusion

Conditional probability allows us to determine the likelihood of an event given the occurrence of another event. In this case, knowing that a student attended the science club provides insight into their likelihood of also participating in the drama club, which is determined to be 50%. This highlights the importance of understanding relationships between different sets of data in probability.

The probability that a student participated in the drama club, given that they attended the science club, is 0.5.

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