the table summarizes the distribution of age and assigned group for 90 participants in a study.\n| |0 - 9…

the table summarizes the distribution of age and assigned group for 90 participants in a study.\n| |0 - 9 years|10 - 19 years|20+years|total|\n|----|----|----|----|----|\n|group a|15|11|4|30|\n|group b|4|5|21|30|\n|group c|11|14|5|30|\n|total|30|30|30|90|\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?\na $\frac{1}{6}$\nb $\frac{1}{4}$\nc $\frac{11}{30}$\nd $\frac{1}{2}$

the table summarizes the distribution of age and assigned group for 90 participants in a study.\n| |0 - 9 years|10 - 19 years|20+years|total|\n|----|----|----|----|----|\n|group a|15|11|4|30|\n|group b|4|5|21|30|\n|group c|11|14|5|30|\n|total|30|30|30|90|\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?\na $\frac{1}{6}$\nb $\frac{1}{4}$\nc $\frac{11}{30}$\nd $\frac{1}{2}$

Answer

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. $\frac{1}{4}$