Insurance. By examining the past driving records of drivers in a certain city, an insurance company has determined the foliowing (empirical) probabilities: Miles Driven per Year 10,000- Less More than 15,000 than 10.000. inclusive, M, 15,000, M, Totals Accident .05 15 20 40 No Accident 10 20 30 60 Totals 15 35 50 1.0 Ifa driver in this city is selected atrandom, what is the probability that a. He or she tives less han 10,000 trvles per year or has an accident? (Type a tlecinal b. He or she dives 10000 or ote nvles per year and has no accidents? 0.50 (Tyoe a decimal

Suppose that 30 percent of an adult population have an infectious disease and 40 percent have achronic disease. Assume that having an infectious disease is independent from having a chronicdisease. For each of the questions below perform the calculation using appropriate statisticalnotation.a. What is the probability that a person selected at random will have both diseases?b. What is the probability of having the infectious disease for people with the chronic disease?c. What is the probability of having the infectious disease for people without the chronic disease?d. What is the probability of not having the infectious disease for people with the chronicdisease?

12. A survey conducted discovered that 63% of all Americans are overweight. Suppose that a number of randomly selected Americans are weighed. The following table may (or may not) be useful: k 0 1 2 3 4 1 4 6 4 1 4Ck (a) Find the probability that the 4th person weighed is the first person to be overweight. (b) Find the probability that it takes less than 4 people to observe the first overweight person. (c) Find the expected value and variance of the number of Americans that would have to be weighed in order to find the first person that was overweight.