Suppose the odds in favour of good weather tomorrow are 3:2
a)What are the odds against good weather tomorrow?
b) What is the probability of good weather tomorrow?

Can you please explain how you got the answer thank you

All the information you need is found here.

Odds - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Odds)

The probability in favor is \frac {p}{1-p}=\frac 32

p is the probability of the event, so solve the above for p.

The probabilities of all possible events add up to 1.