HP 12C: Combination/Binomial Distribution/Negative Binomial Distribution

HP 12C:  Combination/Binomial Distribution/Negative Binomial Distribution

Introduction and Formulas

Combination: Find the number of groups out of a possible set of objects.  The order of objects obtained does not matter. 

Store n in R1, x in R0, and p in R2.  Press [ f ] [ R↓]  (CLEAR PRGM), [ R/S ]

Formula:  COMB(n, x)  = n!/(x! * (n-x)!)

Binomial Distribution:  Find number of successes (x) in a fixed number of trials (n). 

Store n in R1, x in R0, and p in R2.  Press [ g ] [ R↓ ] (GTO) 26, [R/S]

Formula:  COMB(n, x) * p^x * (1 – p)^(n – x)

Negative Binomial Distribution:  Find the number of trials (n) needed to obtain a fixed amount of successes (x).

Store x in R1, n in R0, and p in R2.  Press [ g ] [ R↓ ] (GTO) 43, [R/S]

Formula:  COMB(x – 1, n – 1) * p^(n -1) * (1 – p)^((x - 1) - (n – 1))

In the distribution calculations, p is the probability where 0 ≤ p ≤ 1. 

Note: R3 is used as a flag, which will allowed for branching.

STEP	CODE	KEY
Combination
01	0	0
02	44, 3	STO 3
03	45, 1	RCL 1
04	43, 3	N!
05	45, 0	RCL 0
06	43, 3	N!
07	10	÷
08	45, 1	RCL 1
09	45, 0	RCL 0
10	30	-
11	43, 3	N!
12	10	÷
Flag Testing
13	45, 3	RCL 3
14	1	1
15	30	-
16	43, 35	X=0
17	43, 33, 29	GTO 29
18	45, 3	RCL 3
19	2	2
20	30	-
21	43, 35	X=0
22	43, 33, 49	GTO 49
23	33	R↓
24	33	R↓
25	43, 33, 00	GTO 00
Binomial Distribution
26	1	1
27	44, 3	STO 3
28	43, 33, 03	GTO 03
29	33	R↓
30	45, 2	RCL 2
31	45, 0	RCL 0
32	21	Y^X
33	20	*
34	1	1
35	45, 2	RCL 2
36	30	-
37	45, 1	RCL 1
38	45, 0	RCL 0
39	30	-
40	21	Y^X
41	20	*
42	43, 33, 00	GTO 00
Negative Binomial Distribution
43	1	1
44	44, 30, 1	STO- 1
45	44, 30, 0	STO- 0
46	2	2
47	44, 3	STO 3
48	43, 33, 03	GTO 03
49	33	R↓
50	33	R↓
51	45, 2	RCL 2
52	45, 0	RCL 0
53	21	Y^X
54	20	*
55	1	1
56	45, 2	RCL 2
57	30	-
58	45, 1	RCL 1
59	45, 0	RCL 0
60	30	-
61	21	Y^X
62	20	*
63	43, 33, 00	GTO 00

Examples:

Find the number of combinations of groups of 2 out of possible 12 objects. 

12 [STO] 1, 2 [STO] 0, [ f ] [ R↓ ] (CLEAR PRGM)

Result:  66

Binomial Distribution:  Toss a coin 25 times. (trails) What is the probability of tossing 10 heads? (successes)  Assume a fair coin.  The variables n = 25, x = 10, p = 0.5 

25 [ STO ] 1, 10 [ STO ] 0, 0.5 [ STO ] 2, [ g ] [ R↓ ] (GTO) 26 [ R/S ]

Result:  0.10   (0.0974166393)

Negative Binomial Distribution:  Assume a fair coin. What is the probability that the 15^th tossed of heads comes on the 25^th toss of the coin?  x = 15, n = 25, p = 0.5

25 [STO] 1, 15 [STO] 0, 0.5 [ STO ] 2, [ g ] [ R↓] (GTO) 43 [ R/S ]

Result:  0.12  (0.1168999672)

This blog is property of Edward Shore, 2016.