Using a hypergeometric distribution, calculate the Probability that if you choose 10 items out of 60 with a success count of 24,you will get 4 items of the success count.
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The hypergeometric probability is listed below:

P(x;n,N,k)  =  (kCx) * (N - kCn - x)
  NCn

Calculate Numerator 1

kCx  =  k!
  x!(k - x)!
24C4  =  24!
  4!(24 - 4)!

Calculate k!:

24! = 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 124! = 6.2044840173324E+23

Calculate x!:

4! = 4 x 3 x 2 x 14! = 24

Calculate (x - k)!:

k - x = 24 - 4 = 2020! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 120! = 2432902008176640000
24C4  =  6.2044840173324E+23
  24(2432902008176640000)
24C4  =  6.2044840173324E+23
  5.8389648196239E+19
24C4 = 10626

Calculate Numerator 2

N - kCn - x  =  (N - k)!
  (N - k - n + x)!(n - x)!
60 - 24C10 - 4  =  (36)!
  (60 - 24 - 10 + 4)!(10 - 4)!
36C6  =  (36)!
  (30)!(6)!

Calculate 6!:

6! = 6 x 5 x 4 x 3 x 2 x 16! = 720

Calculate 36!:

36! = 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 136! = 3.719933267899E+41

Calculate 30!:

30! = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 130! = 2.6525285981219E+32
36C6  =  3.719933267899E+41
  720(2.6525285981219E+32)
36C6  =  3.719933267899E+41
  1.9098205906478E+35
36C6 = 1947792

Calculate Denominator

NCn  =  N!
  m!(N - m)!
60C10  =  60!
  10!(60 - 10)!

Calculate N!:

60! = 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 160! = 8.3209871127414E+81

Calculate n!:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 110! = 3628800

Calculate (N - n)!:

50! = 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 150! = 3.0414093201713E+64
60C10  =  8.3209871127414E+81
  3628800(3.0414093201713E+64)
60C10  =  8.3209871127414E+81
  1.1036666141038E+71
60C10 = 75394027566

Calculate Probability

P(4;10,60,24)  =  10626 x 1947792
  75394027566
P(4;10,60,24)  =  20697237792
  75394027566

P(4;10,60,24) = 0.2745

You have 1 free calculations remaining

Calculate the mean μ:
μ  =  nk
  N
μ  =  10 x 24
  60
μ  =  240
  60
μ = 4

Calculate the variance σ2

σ2  =  nk(N - k)(N - n)
  N2(N - 1)
σ2  =  (10)(24)(60 - 24)(60 - 10)
  602(60 - 1)
σ2  =  (240)(36)(50)
  3600(59)
σ2  =  432000
  212400
σ2 = 2.0339

Calculate the standard deviation σ:σ  =  √σ2σ  =  √2.0339σ = 1.4261

What is the Answer?

P(4;10,60,24) = 0.2745

How does the Hypergeometric Distribution Calculator work?

Free Hypergeometric Distribution Calculator - Calculates the probability of drawing x objects out of a subgroup of k with n possibilities in a total group of N using the hypergeometric distribution.This calculator has 4 inputs.

What 3 formulas are used for the Hypergeometric Distribution Calculator?

P(x;n,N,k) = (kCx) * (N - kCn - x)/NCnμ = nk/Nσ2 = nk(N - k)(N - n)/N2(N - 1)

For more math formulas, check out our Formula Dossier

What 10 concepts are covered in the Hypergeometric Distribution Calculator?

combination
a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matternPr = n!/r!(n - r)!
distribution
value range for a variable
event
a set of outcomes of an experiment to which a probability is assigned.
factorial
The product of an integer and all the integers below it
hypergeometric distribution
discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in ndraws, without replacement
mean
A statistical measurement also known as the average
permutation
a way in which a set or number of things can be ordered or arranged.nPr = n!/(n - r)!
probability
the likelihood of an event happening. This value is always between 0 and 1.P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance
How far a set of random numbers are spead out from the mean

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