Please show all the work so I know how to do it. This is for my statistics class.

5) Suppose some medical researchers are testing the effectiveness of a new skin cream designed to treat rashes, but which they suspect may also make rashes worse in some patients. They run an experiment using patients with skin rashes, in which some are given the cream and some are not. For each patient, they record whether the patient's rash got better or worse. The results are in the table below. The expected count is given in parentheses next to the observed count for two of the cells and part of the test statistic formula is shown here. Rash got better Rash got worse Patlent received the 224 (230.85) 74 ( ) 298 skin cream Patlent did not 106 ( ) 22 (28.85) 128 recelve the skin cream m_m a. What is the probability that a randomly selected patient had a rash that got better? (2 points) _ (224 230.85)2 X 230.85 + (22 28.85)2 + + 28.85 b. What is the probability that the rash got worse given that the patient received the cream? (2 points) c. Fill in the other two expected frequencies in the table above and complete the test statistic calculations beside the table. (2 points). d. Use the appropriate hypothesis testing procedure to determine if whether the patient received the skin cream or not and whether the rash got better or worse are dependent or independent variables. Be sure to include all six steps. Note that the critical value here is 3.84. (6 points)