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

The total number of participants at least 10 years old is the sum of those in the 10 - 19 years and 20+ years age - groups. From the table, it is \(40 + 40=80\).

Step2: Find number of participants from group A who are at least 10 years old

The number of participants from group A who are at least 10 years old is the sum of those in the 10 - 19 years and 20+ years age - groups in group A, which is \(18 + 7 = 25\).

Step3: Calculate the conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of frequency - based probability, if \(A\) is the event of selecting a participant from group A and \(B\) is the event of selecting a participant at least 10 years old, then the probability \(P\) of selecting a participant from group A given that the participant is at least 10 years old is \(\frac{\text{Number of group A participants at least 10 years old}}{\text{Total number of participants at least 10 years old}}=\frac{25}{80}=\frac{5}{16}\).

Answer:

B. \(\frac{5}{16}\)