5. In a study following a cohort of people for two decades, researchers looked at the onset of Type II diabetes and nutrition. In this analysis, they look at regular consumption of drinks with added sugar and the development of Type II diabetes. The table below shows the proportion of participants who fell into each group based on whether they consumed drinks with added sugar ("sugary drinks") regularly and whether they developed diabetes. Diabetes No diabetes Consumes sugary drinks regularly 0.12 0.30 Does not consume sugary drinks regularly 0.10 0.48 ________ a. What proportion of participants in the study developed diabetes? ________ b. Find the probability that a person randomly chosen from this study consumed sugary drinks and/or developed diabetes. ________ c. Given that a person from this study consumed sugary drinks, find the probability that the person developed diabetes. 6. It has been estimated that 19% of coal miners who worked in mines in the 1970s die of lung cancer. Consider a simple random sample of 4 coal miners who worked in mines in the 1970s. Let X be the number in the sample who die of lung cancer. _______________________ a. What is the distribution of X? _______b. What is the probability that none of the four die of lung cancer