Mathematics Dictionary
Dr. K. G. Shih
Probability : Hypergeometric
Formula
h(x) = C(k, x)*C(N-k, n-x)/C(N,n)
Symbol Defintion
Example : Sqr(x) = square root of x
Q01 |
- Hypergeometric formula
Q02 |
- Example : A hand of bridge cards have 0 spade
Q03 |
- Example : Take five cards and expect 4 aces
Q04 |
- Example : 24 electric bulbs with 12.5% defective
Q01. Hypergeometric formula
Formula
h(x) = C(k, x)*C(N-k, n-x)/C(N, n)
N = Total sample
n = Take number of samples
k = Take total samples
x = Expect happen events
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Q2. Thae five cards with 4 kings
N = 52 cards
n = Take 5 cards with expected 5th card
k = 5 cards are taken
x = 4 kings
h(x) = C(5, 4)*C(52 - 5, 5 - 4)/C(52, 5)
h(x) = 5*C(47, 1)/C(52, 5)
h(x) = (5*47)/((52*51*50*49*48)/(5!))
h(x) = (5*47)*(5!)/(52*51*50*49*48)
h(x) = (234*120)/(52*51*50*49*48)
N = 52 cards
n = Take 5 cards with any 5th card
k = 4 cards are taken
x = 4 kings
h(x) = C(4, 4)*C(52 - 4, 5 - 4)/C(52, 5)
h(x) = 1*C(48, 1)/C(52, 4)
h(x) = 48/((52*51*50*49)/(4!))
h(x) = 48*(4!))/(52*51*50*49)
h(x) = (48*24)/(52*51*50*49)
h(x) =
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Q4. 24 electric bulbs with 12.5% defective
N = 24 bulbs
n = Take 3 bulbs
k = Defective bulbs = 24*0.125 = 3
x = Expected defective in the 3 bulbs = 0, 1, 2 or 3
Take 3 bulbs without defective one
h(0) = C(3, 0)*C(24 - 3, 3 - 0)/C(24, 3)
h(0) = 1*C(21, 3)/(24, 3)
h(0) = (21*20*19)/(24*23*22)
h(0) =
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AL 17 00. Outline
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