For a given day, temperature can be recorded as hot, mild and cold while weather can be sunny or cloudy. The probability that the temperature is hot, mild and cold are .15, .55 and .30, respectively. Probability that the weather is sunny if the temperature is hot is .67, if the temperature is recorded mild is.36, and if the temperature is cold is.33. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided. (a) List all probabilities given in this problem, expressed in terms of events that you define.
(b) What is the probability that it is a sunny day?
(c) Given that the weather is sunny, what is the probability that the temperature is hot? mild? cold?
(d) Given that the weather is cloudy, what is the probability that the temperature is hot? mild? cold?
(e) Is the cloudy weather independent of hot weather?