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
Download the document here, with gratitude to Datamath:
http://www.datamath.net/Manuals/SR-56_AL_US.pdf
Eddie
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