home > leaked exams > august 2025 international form b (complete exam)\n\n| | 0–9 years | 10–19 years | 20+…

home > leaked exams > august 2025 international form b (complete exam)\n\n| | 0–9 years | 10–19 years | 20+ years | total |\n|--|--|--|--|--|\n| group a | 15 | 18 | 7 | 40 |\n| group b | 5 | 7 | 28 | 40 |\n| group c | 20 | 15 | 5 | 40 |\n| total | 40 | 40 | 40 | 120 |\n\none of these participants will be selected at random. what is the probability of selecting a participant from group a, given that the participant is at least 10 years of age?\n\na $\frac{5}{24}$\nb $\frac{5}{16}$\nc $\frac{9}{20}$\nd $\frac{5}{8}$

home > leaked exams > august 2025 international form b (complete exam)\n\n| | 0–9 years | 10–19 years | 20+ years | total |\n|--|--|--|--|--|\n| group a | 15 | 18 | 7 | 40 |\n| group b | 5 | 7 | 28 | 40 |\n| group c | 20 | 15 | 5 | 40 |\n| total | 40 | 40 | 40 | 120 |\n\none of these participants will be selected at random. what is the probability of selecting a participant from group a, given that the participant is at least 10 years of age?\n\na $\frac{5}{24}$\nb $\frac{5}{16}$\nc $\frac{9}{20}$\nd $\frac{5}{8}$

Answer

Explanation:

Step1: Find number of participants at least 10 years old

Add the totals for 10 - 19 years and 20+ years columns. $40 + 40=80$.

Step2: Find number of participants from Group A at least 10 years old

Add number of participants in Group A for 10 - 19 years and 20+ years. $18 + 7 = 25$.

Step3: Calculate conditional probability

Use the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, the probability of selecting from Group A given at least 10 years old is $\frac{\text{Number in Group A and at least 10}}{\text{Number at least 10}}=\frac{25}{80}=\frac{5}{16}$.

Answer:

B. $\frac{5}{16}$