Buses arrive at a specified stop at 15-minute intervals starting at Î AM. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:30, find the probability that he waits (a) less than 5 minutes for a bus; (b) more than 10 minutes for a bus.

A physics class has 50 students. Of these, 11 students are physics majors and 16 students are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is (Round to three decimal places as needed.) ******************

A man and a woman agree to meet at a certain location about 12:30 P.M. If the man arrives at a time uniformly distributed between 12:15 and 12:45, and if the woman independently arrives at a time uniformly distributed between 12:00 and 1 P.M., find the probability that the first to arrive waits no longer than 5 minutes. What is the probability that the man arrives first?

The probabilities that a particular office phone rings 0, 1, 2, 3 times in half hour are respectively: 0.05, 0.15, 0.21, 0.42. Find the probability that the phone rings at least 4 times between 3:30-4:00 pm.

A certain disease has a prevalence of in a population. The rate of false 4 positives is 10% and and the rate of false negatives is 5%. If you are exposed to the disease, then probability that you contract it is . You can only contract the disease by sharing food. Suppose that you meet 10 people, that each person tests negative for the disease, and that you share food with each of them exactly three times. What is the probability that you contract the disease?

Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.

Solve a,b