Name_____Answers_____________
Homework February 15, 2005
A "Spanish deck" can be created by removing the four tens from a regular 52 card deck. So each Spanish deck has 48 cards. The following questions refer to five card probabilities from a single 48-card Spanish deck.
1. How many combinations are there of five card hands from a Spanish deck?
Combin(48,5)=1,712,304
2. How many pair combinations are there?
12*combin(11,3)*6*4^3=12*165*6*64=760,320
3. How many two pair combinations are there?
combin(12,2)*10*6^2*4=66*10*36*4=95,040
4. How many three of a kind combinations are there?
12*combin(11,2)*4^3=12*55*64=42,240
5. How many straight combinations are there? Assume that the jack comes directly after the 9. For example an 8,9,J,Q,K would count as a straight.
The lowest card can be an A to 9, for 9 different spans. The answer is 9*(4^5-4)=9*1020=9180.
6. How many flush combinations are there?
4*(combin(12,5)-9) = 4*(792-9) = 4*783 = 3132
7. How many full house combinations are there?
12*11*4*6 = 3168
8. How many four of a kind combinations are there?
12*11*4 = 528
9. How many straight flush combinations are there ( not including a royal flush)?
8*4 = 32
10. How many royal flush combinations are there?
4
11. How many ways can you get nothing?
(combin(12,5)-9)*(4^5-4) = (792-9)*(1024-4) = 783*1020=798,660
Following is the pay table for the slot machine Graduation Anxiety.
|
Pay Line |
Pays |
|
Three Graduation caps |
5000 |
|
Three Parent's houses |
2000 |
|
Three Telephones |
1000 |
|
Three Newspapers |
500 |
|
Three job applications |
200 |
|
Three Suits |
100 |
|
Three Resumes |
75 |
|
Three Computers |
50 |
|
Three Pizzas |
25 |
|
Two Pizzas |
5 |
|
One Pizza |
2 |
For the last two wins the pizzas can appear anywhere on the pay line.
Next is the weighting of each symbol for each reel.
|
Symbol |
Reel 1 |
Reel 2 |
Reel 3 |
|
Graduation cap |
1 |
1 |
2 |
|
Parent's house |
2 |
1 |
3 |
|
Telephone |
3 |
3 |
4 |
|
Newspaper |
4 |
3 |
5 |
|
Job application |
5 |
6 |
6 |
|
Suit |
6 |
6 |
7 |
|
Resume |
7 |
8 |
8 |
|
Computer |
8 |
8 |
9 |
|
Pizza |
1 |
1 |
2 |
|
Blank |
27 |
27 |
18 |
|
Total |
64 |
64 |
64 |
Fill in the following table to calculate the return of this slot machine.
|
Payline |
Pays |
Probability Combinations |
Return Combinations |
|
Three Graduation caps |
5000 |
2 |
10000 |
|
Three Parent's houses |
2000 |
6 |
12000 |
|
Three Telephones |
1000 |
36 |
36000 |
|
Three Newspapers |
500 |
60 |
30000 |
|
Three Job applications |
200 |
180 |
36000 |
|
Three Suits |
100 |
252 |
25200 |
|
Three Resumes |
75 |
448 |
33600 |
|
Three Computers |
50 |
576 |
28800 |
|
Three Pizzas |
25 |
2 |
50 |
|
Two Pizzas |
5 |
314 |
1570 |
|
One Pizza |
2 |
15750 |
31500 |
|
Total |
17626 |
244720 |
The total possible outcomes is 643=262,144.
What is the return? ___244720/262144 = 93.35%_______