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! * (nx)!)
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.