out of 125 children at summer camp 45 signed up for swimming 38 for arts and crafts if a child is randomly selected what is the probability that they signed up for swimming if it is known they did not sign up for arts and crafts

P(s) = 45/125 = 0.360
P(A&C) = 38/125 = 0.304
Probability that one is not in Arts and Crafts = 1- P(A&C) = 1-0.304 = 0.696

Therefore,
Probability that the child selected is in swimming when its known they didn't sign for Arts and craft = Probability they signed for swimming * Probability that they didn't sign for Arts and Crafts = 0.360*0.696 = 0.25056