Question

home > leaked exams > june 2025 international form a (complete exam)

	0-9 years	10-19 years	20+ years	total
group b	4	7	24	35
group c	21	11	3	35
total	35	35	35	105

one 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?

a $\frac{5}{21}$
b $\frac{5}{14}$
c $\frac{17}{35}$
d $\frac{5}{7}$

Explanation:

Step1: Find number of participants at least 10 years old

Add participants in 10 - 19 years and 20+ years columns: $35 + 35=70$.

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

Add participants in Group A for 10 - 19 years and 20+ years: $17 + 8 = 25$.

Step3: Calculate conditional probability

Use formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, probability of selecting from Group A given at least 10 years old is $\frac{25}{70}=\frac{5}{14}$.

Answer:

B. $\frac{5}{14}$