The following table reflects the observations made on the color and type of vehicie, if a speeding tícket was recelved (1) or e warning (0), and if there was e prior driving violetion (yes or no). Using the naive Beyes calculation what is the conditional probability of receiving a ticket with a red vehicie given a prior driving violetion. Assume predictor veriables are independent. Color Ticket Туре SUV Prior Yes Red No Red Sport Sport SUV No Green Red

A company did a study of available vacation time for their staff employees over the past years.  They determined the probability a staff employee selected at random has 2 weeks’ vacation was 45%, 1 week vacation 10%, 3 weeks’ vacation 20%, and more than 3 weeks’ vacation was 25%.  The company randomly selects 20 employees.  What is the probability that out of the 20 selected, at least 2 workers have 1 week vacation time?

USA Today (June 6, 2000) gave information on seat belt usage by gender[1]. The proportions in the following table are based on a survey of a large number of adult men and women in the United States.   Male Female Uses Seat Belts regularly 0.1 0.2 Does not use Seat Belts regularly 0.4 0.3   Assume that these proportions are representative of adult Americans and that an adult American is selected at random. What is the probability that the selected adult regularly uses a seat belt? What is the probability that the selected adult does not use a seat belt regularly given that the individual selected is male? What is the probability that the selected adult regularly uses a seat belt given that the selected individual is female? What is the probability that the selected individual is female given that the selected individual regularly uses a seat belt? Are the probabilities from Parts (c) and (d) equal? Write a couple of sentences explaining why this is so.

A survey showed that 81% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction? The probability that no more than 1 of the 20 adults require eyesight correction is (Round to three decimal places as needed.)

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 29 times, and the man is asked to predict the outcome in advance. He gets 25 out of 29 correct. What is the probability that he would have done at least this well if he had no ESP?Probability =