Decision Tree Problem

We are planning an event for next June. If we choose an outdoor venue, we make 350,000 dollars, but if it rains we lose 40,000. If we choose an indoor venue, we make 150,000 rain or not. It rains 1/3 of the night in June.

We can buy a forcast for 15,000. The track record of the forcaster is as follows:

When rain predicted: 80% of the time it actually rained, 20% no rain

When no rain predicted: 70% no rain, 30% rain.

We need to construct a decision tree to tell whether or not to buy the forecast.