please help me build an extended decision tree using the posterior probabilities and emvs for the following question and the payoff table. You are providing advice to novice investor for selecting the best investment choice among two options depicted in the payoff table seen below (showing the expected return of a $1,000 investment in each investment alternative at the end of one year in each of the four economic conditions).

The posterior probabilities for investment A is 565 and EMV for investment A is 435. The posterior probability for investment B is 822 and EMV for investment B is 178

Payoff Table:

Investment A. Investment B Probability

$50 -$70 0.1

$90 $50 0.4

$1200 $270 0.3

$170 $420 0.2