Multinomial Distribution
A recent study of robberies for a certain geographic region showed an average of 1 robbery per 20,000 people. In a city of 80,000 people, find the probability that there are 3 or more robberies.
0.7619
The average number of phone inquiries per day at the Poison Control Center is 4. Find the probability that it will receive 5 calls on a given day.
Ten people apply for a job as assistant manager of a restaurant. Five have completed college, and five have not. If the manager selects 3 applicants at random, find the probability that all 3 are college graduates.
0.083
According to the manufacturer, M&Ms are produced and distributed in the following proportions; 13% brown, 13% red, 14% yellow, 16% green, 20% orange, and 24% blue. In a random sample of 12 M&Ms, what is the probability of having 2 of each color?
0.0025
A sales firm receives, on average, 3 calls per hour on its toll-free number. For any given hour, find the probability that it will receive at most 3 calls.
0.6472
A recent study found that 2 out of every 10 houses in a neighborhood have no insurance. If 5 houses are selected from 10 houses, find the probability that exactly 1 will be uninsured.
0.556
The probability that a person has 1, 2, 3, or 4 prescriptions when he/she enters a pharmacy is 0.5, 0.3, 0.15, or 0.05. For a sample of 10 people who enter the pharmacy, find the probability that 3 will have 1 prescription filled, 3 will have 2 prescriptions filled, 2 will have 3 prescriptions filled, and 2 will have 4 prescriptions filled.
0.0048
If approximately 2% of the people in a room of 200 people are left-handed, find the probability that exactly 5 people there are left-handed.
0.1563
A lot of 12 compressor tanks is checked to see whether there are any defective tanks. Three tanks are checked for leaks. If 1 or more of the 3 is defective, the lot is rejected. Find the probability that the lot will be rejected if there are actually 3 defective tanks in the lot.
0.382