Each night Kim goes to the gym or the pool. If she goes to the gym one night, the probability she goes to the pool the next night is 0.4, and if she goes to the pool one night, the probability she goes to the gym the next night is 0.7. a. Suppose she goes to the gym one Monday night. i. What is the probability that she goes to the pool on each of the next three nights? (The exact value must be given.) ii. What is the probability that she goes to the pool on exactly two of the next three nights? (The exact value must be given.) 1+2=3 marks b. In the long term, what proportion of nights does she go to the pool? (Answer correct to three decimal places.)