3. (8 points) Short answer questions. (a) The letters G, H, I, R, T are randomly permuted. What is the probability that the result is the word R, I, G, H, T? (b) Three fair dice are rolled. What is the probability that they all have the same value? (c) Each time you go to the gym, you have a 20% chance of running into your worst enemy. What is the expected number of trips to the gym before you meet this person? (d) A certain population consists of 40% men and 60% women. Of the men, 20% are left-handed, and of the women, 10% are left-handed. A person is picked at random from this population and is found to be left-handed. What is the probability that this person is female?