A random sample of 250 adults was taken, and they were asked whether they prefer watching sports or opera on television. The following table gives the two-way classification of these adults.
a. If one adult is selected at random from this group, find the probability that this adult
i. Prefers watching opera
ii. Is a male
iii. Prefers watching sports given that the adult is a female
iv. Is a male given that he prefers watching sports
v. Is a female and prefers watching opera
vi. Prefers watching sports or is a male
b. Are the events “female” and “prefers watching sports” independent? Are they mutually exclusive? Explain why or why not.