Probability Functions

SpeQ has functions for probability calculations and for generating random numbers. Probability theory has to do with uncertainty in occurrences.


Overview

You can use the following built-in probability functions.
Function Description
Factorial(x)
x!
Factorial of x. The factorial of a natural number x is the product of all positive integers less than and equal to x. For example 5! = 5*4*3*2*1 = 120. SpeQ can also calculate the factorial value for positive, non-integer values.

nPr(n, r) The number of possibilities for choosing an ordered set of r objects (a permutation) from a total of n objects.
Definition: nPr(n,r) = n! / (n-r)!

nCr(n, r) The number of different, unordered combinations of r objects from a set of n objects.
Definition: nCr(n,r) = nPr(n,r) / r!

Rand Returns a random value between 0 and 1.

Rand({min, } max) If both min and max are given, the function returns a random value (decimal) between min and max.
If only max is given the function returns a random value between 0 and max.

RandInt({min, } max) If both min and max are given, the function returns a random number (integer) between min and max.
If only max is given the function returns a random number between 0 and max.

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Examples

'Examples of using Probability functions

'There are nPr(26, 4) possible ways to write a word with 4 distinct letters.
nPr(26, 4)
       Ans = 358800
'This is equal to:
26*25*24*23
       Ans = 358800

'In the example above there are combinations with the same 4 letters
'but a different order. For example the groups "hgcb" and "bghc". To
'find the number of different combinations we can use the function nCr.
nCr(26, 4)
       Ans = 14950

'Probability of winning Lotto (6 numbers from 44) with 1 ticket.
nCr(44, 6)
       Ans = 7.059052e6

5!
       Ans = 120
5*4*3*2*1
       Ans = 120
(9-2+1)!
       Ans = 40320

Factorial(6)
       Ans = 720
'Using random values:

'Rand gives a random value between 0 and 1
Rand
       Ans = 0.745178223

'Rand(min,max) gives a random value between min and max
Rand(4,10)
       Ans = 5.710388184

'Rand(max) gives a random value between 0 and max
Rand(8)
       Ans = 2.880615234

'RandInt(min,max) gives a random number between min and max
RandInt(4,10)
       Ans = 8

'RandInt(max) gives a random number between 0 and max
RandInt(22)
       Ans = 17
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See Also

Functions overview, Trigonometric Functions Functionstree