Problems 1A and B, 2A and B, and 3

1. Among 124 patients on clinical trial for CALQUENCE, 48 experienced headaches and 2 experienced severe abdominal pain. a) Use this sample group to estimate the probability that a randomly selected person experiences a headache from CALQUENCE. Is this a rare event? b) Use this sample group to estimate the probability that a randomly selected person experiences severe abdominal pain from CALQUENCE. Is this a rare event? 2. A study of effectiveness forthe Moderna COVlD-19 vaccine was conducted within the racially and ethnically diverse membership of Kaiser Permanente in Southern California using specimens collected between December 6 and December 31, 2021. 4269 individuals tested positive for delta variant, 22414 tested positive for omicron variant and 67000 tested negative. Based on this sample group, estimate the probability that a randomly selected KP member: a) Tests positive for a delta infection. Is this a rare event? b) Tests positive for an omicron infection. Is this a rare event? 3. Bumped from a Flight: Among 15,378 Delta airline passengers randomly selected, 3 were bumped from a flight against their wishes (based on data from the U.S. Department of Transportation}. Find the probability that a randomly selected passenger is involuntarily bumped. ls such bumping unusual? Does such bumping pose a serious problem for Delta passengers in general? Why or why not