This is a very favorite problem of mine.

Right, it’s not easy to see all the conditionals.

You actually have to do some algebra to get that the probability of her forecasting rain is ½ ,

and that the probability of her having forecasted rain given that it rains = the probability of her not having forecasted rain given that it does not rain = 2/3

Once this is done, you can easily fill in the tree.

See my website http://duport.com for a hint on the full solution.