DISCRETE MATH REVIEW CH 15 IF WE ROLL

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ACCOMMODATING SPATIAL CORRELATION ACROSS CHOICE ALTERNATIVES IN DISCRETE CHOICE
AN IMPROVEMENT OF DISCRETEDELAYINDEPENDENT STABILITY RESULT FOR NEUTRAL SYSTEMS

BAN530 DISCRETE PROBABILITY DISTRIBUTIONS A RANDOM VARIABLE IS A
BEST PRACTICES FOR LIMITED SCOPE DISCRETE TASK LEGAL SERVICES
CHAPTER 3 EXPECTED VALUE OF A DISCRETE RANDOM VARIABLE

Discrete Math

Discrete Math Review Ch. 15

If we roll a regular six-sided die twice, the probability …

1.) … that at least one of the rolls will land as an even number is

2.) … of both rolls landing even or both rolls landing odd is

If we roll a regular six-sided die three times and note whether it lands as an even number (E) or an odd number (O) on each roll.

3.) Give the sample space for this random experiment.

4.) Give the probability of tossing 3 even rolls.

If an honest coin is tossed twice, …

5.) … the sample space for this random experiment is

6.) … the probability that at least one of the tosses will come up heads is

7.) … the probability that both tosses will come up heads is

8.) … the probability of both tosses coming up the same is

A computer password consists of any five capital letters (A - Z).

9.) How many different passwords are possible?

10.) How many different passwords have no repeated letters?

11.) How many different passwords start with the letter Z?

12.) How many different passwords start with the letter Z and end with the letter W?

A computer password is made up of five characters. Each character can be a capital letter (A - Z) or a digit (0 - 9).

13.) How many different passwords are possible?

14.) How many passwords do not start with the digit 7?

15.) How many passwords start with a digit, rather than a letter?

16.) How many passwords consist entirely of letters?

17.) How many passwords have four letters and only one digit?

18.) How many passwords have three letters and two digits?

Solve the problem.

19.) ₁₄C₂ =

20.) ₁₅P₄ =

21.) ₄C₂ + ₄P₂=

Four drivers (A, B, C, and D) are entered in a race. According to the odds makers, the probability that the driver A will win the race is Pr(A) = 0.4, and the other three drivers all have an equal probability of winning the race.

22.) What is the probability that driver D will win the race?

23.) What are the odds in favor of driver C?

24.) What are the odds against driver B?

A fancy restaurant offers a menu consisting of 5 different appetizers, 3 different salads, 2 different soups, 7 different main courses, and 3 different desserts. The restaurant offers different combinations of "fixed price dinners" on different days of the week.

25.) On Monday through Thursday, the "fixed price dinner" consists of a choice of appetizer, a soup, a main course, and a dessert. How many different "fixed price dinners" are possible on these days?

26.) On Fridays and Saturdays, the "fixed price dinner" consists of a choice of appetizer, either soup or salad, a main course, and a dessert. How many different "fixed price dinners" are possible on Fridays and Saturdays?

KEY:

3/4
2/4
{OOO, OOE, OEO, OEE, EOO, EOE, EEO, EEE}
1/8
{HH,HT, TH, TT}
3/4
1/4
1/2
26 x 26 x 26 x 26 x 26 = 11,881,376
26 x 25 x 24 x 23 x 22 = 7,893,600
1 x 26 x 26 x 26 x 26 = 456,976
1 x 26 x 26 x 26 x 1 = 17,576
36 x 36 x 36 x 36 x 36 = 60,466,176
35 x 36 x 36 x 36 x 36 = 35 x 36⁴
10 x 36 x 36 x 36 x 36 = 10 x 36⁴
26 x 26 x 26 x 26 x 26 = 26⁵
1^st position: 10 x 26 x 26 x 26 x 26 = 10 x 26⁴

2^nd position: 26 x 10 x 26 x 26 x 26 = 10 x 26⁴, Etc.

Total = 10 x 26⁴ times 5 (positions) = 10 x 26⁴ x 5

10 x 10 x 26 x 26 x 26 times 10 combinations of 2 digits filling 5 spaces (₅C₂)= 10² x 26³ x 10
91
32,760
18
0.2
1 to 4
4 to 1
5 x 2 x 7 x 3 = 210
5 x (2+3) x 7 x 3 = 525

CLOSED FORM DISCRETE CHOICE MODELS FRANK S KOPPELMAN AND
CONCRETE EROSION MODELLING BY WATER JET METHOD USING DISCRETE
CONTINUOUS VS DISCRETE PROCESSES THE PROBABILISTIC EVOLUTION OF SINGLE

Tags: discrete math, review, discrete