## Tuesday, May 3, 2022

### HP 32S and HP 32SII Week: Hypergeometric Distribution

HP 32S and HP 32SII Week:  Hypergeometric Distribution

What are the Odds?

The hypergeometric probably function deals with taking samples without replacement.  The trials are not independent.  The probability formula is:

G(S; N, T, M) =

1 ÷ nCr(N, M) * nCr(T, S) * nCr(N-T, M-S)

S = number of successes

N = main population size

T = target's population size

M = sample size

nCr(x, y) = x! ÷ ( y! * (x - y)!)

HP 32S/32SII Program:  Hypergeometric Distribution Probability

Size: 30 bytes

H01 LBL H

H02 INPUT S

H03 INPUT N

H04 INPUT T

H05 INPUT M

H06 RCL N

H07 RCL M

H08 Cn,r

H09 1/x

H10 RCL T

H11 RCL S

H12 Cn,r

H13 ×

H14 RCL N

H15 RCL- T

H16 RCL M

H17 RCL-S

H18 Cn,r

H19 ×

H20 STOP

Examples:

What are the odds that four hearts are dealt out of a five card hand?  Assume a standard, 52 card deck.

S = 4 (4 hearts)

N = 52 (52 cards)

T = 13 (13 hearts)

M = 5 (5 card hand)

Result:  1.07292917E-2 (≈1.07%)

What are the odds that a pair of Kings are dealt out of a five card hand?  Assume a standard, 52 card deck.

S = 2 (2 Kings)

N = 52 (52 cards)

T = 13 (13 hearts)

M = 5 (5 card hand)

Result:  3.99298181E-2 (≈3.99%)

Source:

"Hypergeometric Distribution"  Texas Instruments Programmable Slide-Rule SR-56 Applications Library  pp. 58-59 Texas Instruments, 1976