Question

1. The sample space contains 5 As and 7 Bs. What is the probability that a randomly selected set of 2 will include 1 A and 1 B?

2. In a city of 120,000 people there are 20,000 Norwegians. What is the probability that a randomly selected person from the city will be Norwegian

4. A corporation receives a particular part in shipments of 100. Research indicated the probabilities shown in the accompanying table for numbers of defective parts in a shipment.

a. What is the probability that there will be fewer than three defective parts in a shipment?

b. What is the probability that there will be more than one defective part in a shipment?

c. The five probabilities in the table sum to 1. Why must this be so?

5. The probability of A is 0.60, the probability of B is 0.40, and the probability of either is 0.76. What is the probability of both A and B

Market research in a particular city indicated that during a week, 18% of all adults watch a television program oriented to business and financial issues, 12% read a publication oriented to these issues, and 10% do both.

a. What is the probability that an adult in this city who watches a television program oriented to business and financial issues reads a publication oriented to these issues?

b. What is the probability that an adult in this city who reads a publication oriented to business and financial issues watches a television program oriented to these issues?

9. At the beginning of winter, a homeowner estimates that the probability is 0.4 that his total heating bill for the three winter months will be less than $380. He also estimates that the probability is 0.6 that the total bill will be less than $460.

a. What is the probability that the total bill will be between $380 and $460?

b. Given no further information, what can be said about the probability that the total bill will be less than $400?

10. Let the random variable X follow a normal distribution with m = 80 and s2 = 100.

a. Find the probability that X is greater than 60.

b. Find the probability that X is greater than 72 and less than 82.

c. Find the probability that X is less than 55.

d. The probability is 0.1 that X is greater than what number?

e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?

11. Below the age 35, who are infected by Covid-19, there is a 0.8 probability of  success in surviving and recovering (This often depended on the health background status of the person).

Calculate the probability of  the recovering successes  of 7 people  in 10 infected aged below 35.

12.  The internet connection failures (disconnections) happened with an average of 3 failures every twenty minutes in a day  based on  a Poisson distribution, calculate the probability of no more disconnections in a day.

13. On weekdays, a bus arrives at the bus top every 20 minutes between 8 a.m. and 10 p.m. Passengers arrive at the bus stop at random times. The time that a person waits is uniformly distributed from 0 to 20 minutes.

1. Draw a graph of this distribution.
2. Show that the area of this uniform distribution is 1.00.
3. What is the mean waiting time? What is the standard deviation of the waiting time?
4. What is the probability a student will wait between 10 and 20 minutes?

Answer 1