A conference began at noon with two parallel sessions. The session on portfolio management was attended by 40% of the delegates, while the session on chartism was attended by 50%. The evening session consisted of a talk titled “Is the Random Walk Dead?” This was attended by 80% of all delegates.a. If attendance at the portfolio management session and attendance at the chartism session are mutually exclusive, what is the probability that a randomly chosen delegate attended at least one of these sessions?b. If attendance at the portfolio management session and attendance at the evening session are statistically independent, what is the probability that a randomly chosen delegate attended at least one of these sessions?c. Of those attending the chartism session, 75% also attended the evening session. What is the probability that a randomly chosen delegate attended at least one of these two sessions?

From experience, the human resources director of a certain company estimates that, for a particular job opening, 80% of the applicants are qualified.  To help in the selection process, a test has been designed so that a qualified applicant has an 85% chance of passing the test, while an unqualified applicant has only a 5% chance of passing.  An applicant is selected at random. a. What is the probability that the applicant is qualified and will pass the test? b. If the applicant passed the test, what is the probability that he or she is unqualified for the job?

3.  An airline tracks data on the flight arrivals. Over the past 6 months, 65 flights on one route around early, 130 arrived on time,   15 were late,  and 30 were cancelled. A. What is probability the flight is early? On time? Late? Canceled? B. Are thes outcomes exclusive?  C. What id the probability that a flight is either early or on time?

1. Researchers are interested in the relationship between vaping and upper respiratory infections. Suppose that 15% of their population of interest has vaped in the past year and 25% have had an upper respiratory infection in the past year. In addition, they know that 10% have both vaped and had an upper respiratory infection in the past year. What percent of the population has neither vaped nor had an upper respiratory infection in the past year? b. What is the probability of having an upper respiratory infection in the past year given that the person has vaped in the past year? What is the complement of the event in part b)? Be sure to interpret this probability in the context of the problem. a. C. d. What is the probability of having an upper respiratory infection in the past year given that the person has not vaped in the past year? Are the two events independent? Be sure to justify your answer. Based on your calculations what can you conclude about the relationship between vaping…