SAT Question 89f20d9e: Probability And Conditional Probability answer and explanation with Desmos solution

Choice B is correct. Since the participant will be selected at random, the probability of selecting a participant from group A, given that the participant is at least $10$ years of age, is equal to the number of participants from group A who are at least $10$ years of age divided by the total number of participants who are at least $10$ years of age. Based on the table, in group A, there are $17$ participants who are $10$ – $19$ years of age and $8$ participants who are $20+$ years of age. Therefore, there are a total of $17+8$, or $25$, participants in group A who are at least $10$ years of age. Based on the table, of the total number of participants, there are $30$ participants who are $10$ – $19$ years of age and $30$ participants who are $20+$ years of age. Therefore, a total of $30+30$, or $60$, of the participants are at least $10$ years of age. Thus, the probability of selecting a participant from group A, given that the participant is at least $10$ years of age, is $\frac{25}{60}$, or $\frac{5}{12}$.