Of all cities in the United States, Amherst, New York, has the fewest number of days per year clear of clouds, 4.4.33 Other cities with very few clear days include Buffalo, New York, Lakewood, Washington, and Seattle, Washington. Suppose a random year is selected.
a. What is the probability that Amherst will have exactly three days clear of clouds?
b. What is the probability of fewer than six days clear of clouds?
c. What is the probability of at least nine days clear of clouds?
d. Suppose that between 2 and 10 (inclusive) days are clear of clouds. What is the probability of more than five days clear of clouds?
Bad weather is to blame for some of the worst highway crashes in Canada. In December 2012 there was a 27-vehicle pile-up on Highway 40, and in February 2013 a 50-car pile-up shut down Highway 401 near Woodstock, Ontario. Highway 63 in Alberta has a notorious reputation; there are approximately four accidents every week on this road.34 Suppose a week is randomly selected.
a. Find the probability that there are no more than four crashes.
b. Find the probability that the number of crashes is more
c. To obtain government funding for safety improvements, there must be five weeks in a row with six or more crashes. What is the probability of this happening?
On a Friday night in late March 2013, there were hundreds of reports of meteor sightings along the East Coast of the United States. People from North Carolina to Canada contacted the American Meteor Society to report what they saw and heard. Suppose that in a group of 25 people at the National Mall, 15 actually saw the meteor. A patrolman randomly selects five people from this group.
a. What is the probability that none of the five people saw the meteor?
b. What is the probability that at least four people saw the meteor?
c. What is the probability that at most two people saw the meteor?