Question

home > leaked exams > august 2025 international form b (complete exam)

	0–9 years	10–19 years	20+ years	total
group b	5	7	28	40
group c	20	15	5	40
total	40	40	40	120

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 $\frac{5}{24}$
b $\frac{5}{16}$
c $\frac{9}{20}$
d $\frac{5}{8}$

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. $\frac{5}{16}$