Please answer all questions, thank you

Suppose the weather and the animals obey the following rules. 0 The weather of each day is independent of previous days. 0 Each day is either sunny or cloudy (but not both); the probability of a day being sunny is g. o The temperature of a day is exactly one of hot, mom or cold. A sunny day is either hot or warm, where the probability that a sunny day is hot is i. A cloudy day is either warm or cold. where the probability that. a cloudy day is cold is %. 0 Whether an animal appears in a clay depends only on the temperature of that day. A tortoise appears only on a hot or warm day. The probability that a tortoise appears on a hot day is g, and the probability that it appears on a warm day is %. A hare appears only on a warm or cold day. The probability that a hare appears on a warm day is a. and the probability that. it appears on a cold day is i. (a) Consider the following scenarios on some given day. (i) (3 pt.) What is the probability that a tortoise appears? (ii) (3 pt) Is the event. that \"a tortoise appears\" independent of the event that "'a hare ap- pears\"? Prove your answer. (iii) (3 pt) Suppose a given day is cold. Are the events \"a tortoise appears\" and "'a hare appears\" independent? Prove your answer. (iv) (3 pt} Suppose on a given day, a tortoise appears and a hare does not. appear. \\Vhat is the probability that the day is sunny