On any given Saturday, Daina may go on a bike ride in the river valley. If it is sunny outside there is a 0.75 probability that Daina will go for a bike ride. If it is not sunny, the probability that Daina goes for a bike ride is 0.35. Next Saturday, the forecast says the probability it will be sunny is 0.60.

Given that Daina goes for a bike ride next Saturday, the probability it was sunny is

AND

On any given Saturday Ron may go for a bike ride along the beach. If it is sunny outside, there is a 0.79 probability that he will go for a bike. If it is not sunny, the probability that Ron goes for a bike is 0.21. Next Saturday, the weather channel predicts a probability of 0.81 that it will be sunny.

Given that Ron goes for a bike next Saturday,Determine the probability that

it was sunny outside? Illustrate this problem with a diagram and evaluate

your answer to the nearest hundredth.