Answer:
To find the probability that a marathon runner is female given that she is an adult, we need to use conditional probability. We can use the following formula:
P(Female | Adult) = P(Female and Adult) / P(Adult)
We are given the number of marathon participants in the adult and female age groups, so we can calculate the probabilities as follows:
P(Female and Adult) = 113
P(Adult) = 90 + 113 = 203
Therefore, the probability that a marathon runner is female given that she is an adult is:
P(Female | Adult) = 113 / 203 ≈ 0.5567 or approximately 55.67%