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 15th tossed of heads comes on the 25th 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.