4. Consider the following results of a study that was described in an article entitled “Caffeine as a Protective Factor in Dementia and Alzheimer's Disease.” [Note: Dementia is loss of or damage of mental abilities, such as memory and the ability to understand and reason, among other symptoms.] The study followed 1,409 adults for 21 years. During that time, 61 adults developed dementia. The researchers classified the research participants into three categories, based on coffee consumption levels: Low (0 to 2 cups per day), Medium (3 to 5 cups per day) and High (6 or more cups per day). Low Coffee Consumption Medium Coffee Consumption High Coffee Consumption Total 20 20 21 61 Developed Dementia Did not Develop Dementia 204 622 522 1,348 Total 224 642 543 1,409 Calculate the following conditional probabilities. Show all work: (a) P(developed dementia | low coffee consumption). (b) P(developed dementia medium coffee consumption). (c) P(developed dementia | high coffee consumption). (d) Which group had the lowest rate of developing dementia?