Chez Scheme provides a built-in procedure random that is often helpful in modelling real-world phenomena that do not follow any obvious algorithms and are not predictable.

When the random procedure is given an exact positive integer as argument, it returns some non-negative integer less than the argument, but not always the same one. Over a long series of calls, you'll get back each non-negative integer less than the argument about equally often. So, for example, the call (random 20) always yields some integer in the range from 0 to 19, and over a long series of calls you can expect each of those values to be returned about one-twentieth of the time.

(random 20) ===> 4
(random 20) ===> 17
(random 20) ===> 16

When the argument to random is an inexact positive real (typically specified by a numeral containing a decimal point), random returns some non-negative real value less than the argument. Over a long series of identical calls, the values returned will be distributed approximately evenly throughout the interval from 0.0 (inclusive) to the value of the argument (exclusive).

(random 1.5) ===> 0.046003446339158316
(random 1.5) ===> 1.3329912409120568
(random 1.5) ===> 1.4584015323556465
(random 1.5) ===> 0.14671341559491913
(random 1.5) ===> 1.1500817949427606

A typical use of random is to simulate the rolling of an ordinary six-sided die. The roll-a-die procedure returns a random integer in the range from 1 to 6:

(define roll-a-die
  (lambda ()
    (+ 1 (random 6))))

Note that roll-a-die takes no arguments. To invoke it, just write its name between parentheses: (roll-a-die).

Another common application of random is to select an element at random from a non-empty list. The random-element procedure performs this operation on a given list:

(define random-element
  (lambda (ls)
    (list-ref ls (random (length ls)))))

(random-element '(a b c d e f g)) ===> c
(random-element '(a b c d e f g)) ===> f
(random-element '(a b c d e f g)) ===> b
(random-element '(111 112 114 118 126)) ===> 112
(random-element '(only)) ===> only

In English: To choose a random element from a list, obtain a random non-negative integer less than the length of that list and select the element at that position in the list.

1. Write a toss-a-coin procedure that takes no arguments and returns either the string "heads" or the string "tails", about equally often over a long series of calls.

2. Write a procedure named roll-two-dice that takes no arguments, simulates the independent rolling of two dice, and returns the total of the numbers on the faces that turn up.

This document is available on the World Wide Web as

http://www.math.grin.edu/courses/Scheme/random-number-generation.html