According to a recent Harris Poll of adults with pets, the probability that the pet owner cooks especially for the pet either frequently or occasionally is 0.24.

(a) From this information, can we conclude that the probability a male owner cooks for the pet is the same as for a female owner? Explain.

(b) According to the poll, the probability a male owner cooks for his pet is 0.27, whereas the probability a female owner does so is 0.22. Let's explore how such probabilities might occur. Suppose the pool of pet owners surveyed consisted of 200 pet owners, 100 of whom are male and 100 of whom are female. Of the pet owners, a total of 49 cook for their pets. Of the 49 who cook for their pets, 27 are male and 22 are female. Use relative frequencies to determine the probability a pet owner cooks for a pet, the probability a male owner cooks for his pet, and the probability a female owner cooks for her pet.