Improvement No improvement Total Allergy drug 75 55 130 Placebo 42 58 100 Control 31 49 80 Total 148 162 310 A. What is the probability that a randomly selected person in the study was given either the d placebo? State whether events are overlapping or non-overlapping? And why? P(A) P(B) P(A or B) B. What is the probability that a randomly selected person either improved or did not improve? Sta events are overlapping or non-overlapping? And why? P(A) P(B) P(A or B) C. What is the probability that a randomly selected person either was given the drug or improved? State w events are overlapping or non-overlapping? And why? P(A) P(B) P(A and B) P(A or B) D. What is the probability that a randomly selected person was given the drug and improved? State whethe are dependent or not? And why? P(A) P(B given A) P(A and B) study was given either the drug or the nd why? oved or did not improve? State whether the drug or improved? State whether ug and improved? State whether events A) Calculate the number of ways in which 5 lottery balls can be selected from a pool of 44 balls. What is the probability of winning such a lottery (by matching all five numbers?). Technique: nCr Probability B) Calculate the number of ways in which 6 lottery balls can be selected from a pool of 40 balls. What is the probability of winning such a lottery (by matching all six numbers?). Technique: nCr Probability C) Which lottery offers a better chance of winning? e selected from a pool of y (by matching all five e selected from a pool of y (by matching all six Compare the doubling times found with the approximate and exact doubling time formulas. Then u the exact doubling time formula to answer the given question. Inflation is causing prices to rise at a rate of 12% per year. For an item that costs $500 today, what will the price be in 4 years? Round values to two decimal places. approximate doubling time exact doubling time t initial value new value time formulas. Then use using prices to rise at a e in 4 years? Round Assume the carrying capacity of the earth is 12 billion. Use the 1960s peak annual growth rate of 2. 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate co growth rate of about 1.2% per year? Round values to four decimal places. r (base growth rate) current population (billions) predicted current growth rate 2.1 6.8 0.9100 s peak annual growth rate of 2.1% and population of es the predicted growth rate compare to the actual aces