Question

the table summarizes the distribution of age and assigned group for 90 participants in a study.

	0 - 9 years	10 - 19 years	20+years	total
group b	4	5	21	30
group c	11	14	5	30
total	30	30	30	90

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 $\frac{1}{6}$
b $\frac{1}{4}$
c $\frac{11}{30}$
d $\frac{1}{2}$

Explanation:

Step1: Find number of participants at least 10 years old

Add the totals of 10 - 19 years and 20+ years columns: $30 + 30=60$.

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

Add the number of participants in Group A for 10 - 19 years and 20+ years: $11 + 4 = 15$.

Step3: Calculate conditional probability

Use the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, it's $\frac{\text{Number in A and B}}{\text{Number in B}}$. So the probability is $\frac{15}{60}=\frac{1}{4}$.

Answer:

B. $\frac{1}{4}$