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Math·Problem-Solving and Data Analysis·Probability and conditional probability

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Group	0-9 years	10-19 years	20+ years	Total
Group A	15	16	9	40
Group B	5	9	26	40
Group C	20	15	5	40
Total	40	40	40	120

The table summarizes the distribution of age and assigned group for $120$ participants in a study.

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

$\frac{2}{5}$

D

$\frac{5}{8}$