A marketing survey is taken among fast food customers to determine their preference for hot dogs or pizza. Of the 200 respondents selected, 75 were children and 125 were adults. 80 of the respondents preferred pizza and 55 of the children preferred hot dogs.
a. Find the probability that a randomly selected respondent is an adult.
b. Find the probability that a randomly selected respondent prefers hot dogs.
c. Given that the randomly selected person is a child, find the probability that the respondent prefers hot dogs.
d. Find the probability that a child prefers either hot dogs or pizza.