11. 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?
Answer: D
The probability that a student participated in the drama club, given that they attended the science club, is 0.5.
To find this probability, we use the formula for conditional probability. The probability of participating in the drama club given participation in the science club is calculated as the probability of both events occurring divided by the probability of the science club participation.
A) 0.15
This option represents the probability of students participating in both clubs, which is not relevant to the question of conditional probability. While 15% of students participate in both clubs, it does not account for those who are in the science club alone, making this option incorrect.
B) 0.3
This option indicates the overall participation in the science club. However, it does not provide the probability of drama club participation among those already in the science club. Thus, this option does not answer the question and is therefore incorrect.
C) 0.4
This option suggests a probability that is not derived from the given participation figures. It does not reflect the correct calculation needed for the conditional probability. Hence, this option is also incorrect.
D) 0.5
This option accurately represents the conditional probability calculated by dividing the probability of participating in both clubs (15%) by the total probability of participating in the science club (30%). Therefore, 0.15 divided by 0.30 equals 0.5, making this option correct.
Conclusion
The correct answer, 0.5, reflects the precise calculation of conditional probability based on the participation rates of the clubs. The other options fail to provide the proper context needed to determine the probability of drama club participation given attendance in the science club, making them incorrect. Thus, Option D is definitively the right choice.