Question $4(35$ Points$)$

Iman just got a new job and can transfer some of his retirement funds from his previous employer into a new short$-$term money market investment fund.

Based on his investment amount, the fund will pay him $$100,000$ after one year if the market is favorable, and he will lose $$50,000$ if the market is unfavorable. If he doesn$$t invest, Iman will have no profit or loss.

The investment company offering the fund offers two market forecast guides. The Basic Guide is free and predicts a favorable market $65\%$ of the time. The Basic Guide predictions are correct $75\%$ of the time.

The company offers a Premium Guide for $$8,500.$ The Premium Guide also predicts a favorable market $65\%$ of the time but its predictions are correct $90\%$ of the time.

Develop a decision tree to map Iman$$s choices and determine the best course of action.