A fisherman takes his boat out on a river to catch some trout. Assume that 28% of captured fish are trout, 45% are female, and 12% are female trout. Let T represent the event that a captured fish is a trout, and F represent the event that a captured fish is female. In each part of this question, you must first express each probability in terms of the events T and F and justify any computation using a formula. Do not define any additional events. (a) Express each of the three probabilities listed above in terms of the events T and F. (b) Are T and F mutually exclusive events? Explain using the probabilities you stated in part (a). (c) What proportion of all captured fish are not trout? (d) What is the probability a captured fish will satisfy at least one of the characteristics of being a trout or being a female? (e) What proportion of captured fish are female but are not trout? (f) What is the probability that a captured fish will be neither a trout nor a female?