Sarah is training for a half-marathon and incorporated regular running as part of her training routine. If the weather is sunny, she's inclined to go for a run with a probability of 0.7. However, if it's not sunny, her likelihood of going for a run decreases to 0.2. Let's assume the probability of a sunny day is 0.85. Let S represent the event of sunny weather, and NS represent the event of non-sunny weather. Let R denote the event that Sarah goes for a run, and NR denote the event that Sarah does not go for a run. ------------------------------------------------------------- a) Out of the days that Sarah goes for a run, the proportion of days the weather is sunny can be expressed as follows: * give me the equation* b) Given that Sarah does not go for a run, the probability that the weather was not sunny can be expressed as: * give me the equation* c)What is the probability that Sarah goes for a run and the weather is sunny? d) What is the probability that Sarah goes for a run on any given day? e) Assuming Sarah goes for a run, what is the probability that the weather is