You must decide whether to hold a fundraising event indoors or outdoors. There is a $35\%$ likelihood of rain. If held outdoors, you estimate you can expect $1,000$ attendees. If held indoors, you have a much smaller capacity. The indoor venue costs $$2,000$ to rent and has a capacity of $500.$ If the weather is bad, you think you can sell out an indoor event. But, if the weather is nice, you may get lower turnout to an indoor event, and cannot expect more than $400$ to show up$.$ An outdoor venue costs only $$500$ for cleanup fees but is non$-$refundable. However, if it rains, you risk having to cancel. You could rent a big tent which would hold some of the activities if it were held outdoors. The tent costs $$4,000,$ plus $$1,000$ to set up and take down, day$-$of$.$ If you rent the tent and it does not rain at all, you could decide not to put up the tent. If it turns out to be rainy, having a tent will likely attract at least $300$ attendees. If you have no tent and it does rain, you will have to cancel the event and you estimate it will cost $$1,000$ in administrative fees and non$-$refundable food and DJ deposits. You think you can sell tickets for $$20$ regardless of whether it is indoors or outdoors.

a$)$ Build a decision tree to represent your decisions

b$)$ What would your decisions be$?$ Why?