Question

Students must show work to receive full credit.

1. Differentiate “Empirical Probability” and “Classical Probability”.

2. Define “Independent Events”, “Mutually Exclusive Events”, and “Collectively Exhaustive Events”.

3. Suppose there are 15 red marbles and 5 blue marbles in a box. (3.a) If an individual randomly selects two marbles without replacement, what is the probability that both marbles are red? (3.b) If an individual randomly selects two marbles with replacement, what is the probability that both marbles are red?

4. Solve for 150C145.

5. A survey of top executives revealed that 15% of them regularly read Time magazine, 25% read Newsweek, and 50% read U.S. News & World Report. Five percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?

6. A study by the National Park Service revealed that 75% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 30% visit the Grand Tetons, and 25% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?

7. A lamp manufacturer designed six lamp bases, two lampshade and four patterns that could be used together. How many different arrangements of base, lampshade, and patterns can be offered?

8. If one selects five cards from a standard deck of cards without replacement, (8a) How many permutations are possible? (8b) How many combinations are possible?

9. Consider the following table: Male Female Total

Democrat 30 60 90

   Republican 40 55 95

Independent 10 5 15

Total 80 120 200

(9.a) What is probability of person of being a Democrat?

(9.b) What is the probability of being a Democrat given one knows the person is a Male?

(9.c) What is the probability of being a Democrat given one knows the person is a Female?

(9.d) What is the probability of a person being a Male and a Democrat?

(9.e) What is the probability of a person being a Male or a Democrat?

10. A tire manufacturer advertises, "The median life of our new all-season radial tire is 75,000 miles. An immediate adjustment will be made on any tire that does not last 75,000 miles." A customer purchased four of these tires. What is the probability that two of the four tires will wear out before traveling 75,000 miles?

11. Explain the reason that the following is not an acceptable probability distribution. P(X) = 0.25 if X = 1, 3, 5, 7, 9 P(X) = 0.00 Otherwise

12. The total number of heads for a coin flipped four times is a random variable X with the following probability distribution. P(X=0) = 0.0625 P(X=1) = 0.2500 P(X=2) = 0.3750 P(X=3) = 0.2500 P(X=4) = 0.0625 Draw a graph of the density function.

13. The total number of heads for a coin flipped four times is a random variable X with the following probability distribution. P(X=0) = 0.10 P(X=1) = 0.40 P(X=2) = 0.20 P(X=3) = 0.10 P(X=4) = 0.20 Determine the mean and variance of X.

14. Create a discrete probability function with positive probabilities for X=1, X=2, X=7, and X=100, and zero probability for all other values of X.

15. If random variable X has binomial distribution with n=5 and π = 0.100, determine the probability of X = 2.

16. If random variable X has a Poisson distribution with n=5 and π = 0.100, determine the probability of X = 2.

17. If random variable X has binomial distribution with n=6 and π = 0.200, determine the mean the of X.

18. If random variable X has Poisson distribution with n=3 and π = 0.100, determine the variance of X.

19. Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within four weeks of the purchase date. Their records reveal that customers return 20% of the diamond wedding rings. Five different customers buy a wedding ring. What is the probability that either one or two customer of the five customers return a ring?

20. Consider the experiment where one randomly rolls two die and the sums of the total number of dots. Provide a list of all possible outcomes and three examples of events.

Answer 1

solution: (1) classical probability : It measures the ? likelihood of events in classics also means that each experiment will contain elements are are equally likely to happen. events in classic sence, it Empirical probability: It is based on the past experience. The emporiçal probability is also known as relahire frequency or Experimental probability. Independent eront: Happening of me event does not effect the other. Muthual Exlusive :- Both the event don't contaims any element in commm. a)? collectively Exhaustive :- Set of event is collectively Exhaustive it allegt one of event must occur. (211) och ny do 5 Blues Is Red 00000 - PURPO P(RIP). * ) wich oploceme me

(A) 150 C,as = 150! 145! X (150-145) ! - 150! = 1591600050 145) 5!