Question 1: Experiment Analysis

You would like to analyze the effectiveness of two diet plans aimed at weight-loss. You design a randomized experiment in which 30 individuals are randomly assigned to one of two diet plans. Each individual follows the diet plan for one month, after which you record whether atleast 4 lbs were lost over the month. Let D₁ and D₂ be the events of being as- signed to plan 1 and 2 respectively. Let S be the event that the individual lost atleast 4 lbs

in one month, and F be the event that they did not. The findings from the experiment are summarized in the probability tree below.

a. Complete the probability tree.

b. Compare P(SD₁) and P(S|D₂). Which diet plan seems to be more effective?

b. Find P(D₁|S) and P(D₂|S).