Problem 4: In the 1860 s, Joseph Lister conducted a landmark experiment to investigate the benefits of sterile technique in surgery. At the time, it was not customary for surgeons to wash their hands or instruments prior to operating on patients. Lister developed a new operating procedure in which surgeons were required to wash their hands, wear clean gloves, and disinfect surgical instruments with carbolic acid. This new procedure was compared to the old, non-sterile procedure and Lister recorded the number of patients in each group that lived or died. Putting Lister's results in a contingency table, we have: (a) Compute the corresponding probability table showing all marginal totals. (b) Provide probabilities of: (i) Sterile and living (ii) Sterile and dead (iii) Control and living (iv) Control and dead (v) Living (vi) Dead (vii) Survived given sterile (viii) Died given control For probabilities (i) through (viii), for each mention which ones are joint, marginal and conditional. [Make sure to define probability events appropriately based on the context of the problem and show all steps for full credit.].