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# Write a function that generates one of 3 numbers according to given probabilities

You are given a function rand(a, b) which generates equiprobable random numbers between [a, b] inclusive. Generate 3 numbers x, y, z with probability P(x), P(y), P(z) such that P(x) + P(y) + P(z) = 1 using the given rand(a,b) function.
The idea is to utilize the equiprobable feature of the rand(a,b) provided. Let the given probabilities be in percentage form, for example P(x)=40%, P(y)=25%, P(z)=35%..

Following are the detailed steps.
1) Generate a random number between 1 and 100. Since they are equiprobable, the probability of each number appearing is 1/100.
2) Following are some important points to note about generated random number ‘r’.
a) ‘r’ is smaller than or equal to P(x) with probability P(x)/100.
b) ‘r’ is greater than P(x) and smaller than or equal P(x) + P(y) with P(y)/100.
c) ‘r’ is greater than P(x) + P(y) and smaller than or equal 100 (or P(x) + P(y) + P(z)) with probability P(z)/100.

## C++

 `// C++ code for approach` `// This function generates 'x' with probability px/100, 'y' with ` `// probability py/100  and 'z' with probability pz/100:` `// Assumption: px + py + pz = 100 where px, py and pz lie ` `// between 0 to 100 ` `int` `random(``int` `x, ``int` `y, ``int` `z, ``int` `px, ``int` `py, ``int` `pz)` `{       ` `        ``// Generate a number from 1 to 100` `        ``int` `r = ``rand``(1, 100);` `     `  `        ``// r is smaller than px with probability px/100` `        ``if` `(r <= px)` `            ``return` `x;`   `         ``// r is greater than px and smaller than or equal to px+py ` `         ``// with probability py/100 ` `        ``if` `(r <= (px+py))` `            ``return` `y;`   `         ``// r is greater than px+py and smaller than or equal to 100 ` `         ``// with probability pz/100 ` `        ``else` `            ``return` `z;` `}`   `// This code is contributed by ajaymakvana.`

## C

 `// This function generates 'x' with probability px/100, 'y' with ` `// probability py/100  and 'z' with probability pz/100:` `// Assumption: px + py + pz = 100 where px, py and pz lie ` `// between 0 to 100 ` `int` `random(``int` `x, ``int` `y, ``int` `z, ``int` `px, ``int` `py, ``int` `pz)` `{       ` `        ``// Generate a number from 1 to 100` `        ``int` `r = ``rand``(1, 100);` `     `  `        ``// r is smaller than px with probability px/100` `        ``if` `(r <= px)` `            ``return` `x;`   `         ``// r is greater than px and smaller than or equal to px+py ` `         ``// with probability py/100 ` `        ``if` `(r <= (px+py))` `            ``return` `y;`   `         ``// r is greater than px+py and smaller than or equal to 100 ` `         ``// with probability pz/100 ` `        ``else` `            ``return` `z;` `}`

## Java

 `// This function generates 'x' with probability px/100, 'y'` `// with probability py/100  and 'z' with probability pz/100:` `// Assumption: px + py + pz = 100 where px, py and pz lie` `// between 0 to 100` `static` `int` `random(``int` `x, ``int` `y, ``int` `z, ``int` `px, ``int` `py,` `                  ``int` `pz)` `{` `    ``// Generate a number from 1 to 100` `    ``int` `r = (``int``)(Math.random() * ``100``);`   `    ``// r is smaller than px with probability px/100` `    ``if` `(r <= px)` `        ``return` `x;`   `    ``// r is greater than px and smaller than or equal to` `    ``// px+py with probability py/100` `    ``if` `(r <= (px + py))` `        ``return` `y;`   `    ``// r is greater than px+py and smaller than or equal to` `    ``// 100 with probability pz/100` `    ``else` `        ``return` `z;` `}`   `// This code is contributed by subhammahato348.`

## Python3

 `import` `random`   `# This function generates 'x' with probability px/100, 'y' with ` `# probability py/100  and 'z' with probability pz/100:` `# Assumption: px + py + pz = 100 where px, py and pz lie ` `# between 0 to 100 ` `def` `random(x, y, z, px, py, pz):  ` `    `  `    ``# Generate a number from 1 to 100` `    ``r ``=` `random.randint(``1``, ``100``)` `    `  `    ``#  r is smaller than px with probability px/100` `    ``if` `(r <``=` `px):` `        ``return` `x` `    `  `    ``# r is greater than px and smaller than ` `    ``# or equal to px+py with probability py/100 ` `    ``if` `(r <``=` `(px``+``py)):` `        ``return` `y` `        `  `    ``# r is greater than px+py and smaller than` `    ``# or equal to 100 with probability pz/100 ` `    ``else``:` `        ``return` `z` `    `  `# This code is contributed by rohan07`

## C#

 `// This function generates 'x' with probability px/100, 'y'` `// with probability py/100  and 'z' with probability pz/100:` `// Assumption: px + py + pz = 100 where px, py and pz lie` `// between 0 to 100` `static` `int` `random(``int` `x, ``int` `y, ``int` `z, ``int` `px, ``int` `py,` `                  ``int` `pz)` `{` `    ``// Generate a number from 1 to 100` `    ``Random rInt = ``new` `Random();` `    ``int` `r = rInt.Next(0, 100);`   `    ``// r is smaller than px with probability px/100` `    ``if` `(r <= px)` `        ``return` `x;`   `    ``// r is greater than px and smaller than or equal to` `    ``// px+py with probability py/100` `    ``if` `(r <= (px + py))` `        ``return` `y;`   `    ``// r is greater than px+py and smaller than or equal to` `    ``// 100 with probability pz/100` `    ``else` `        ``return` `z;` `}`   `// This code is contributed by subhammahato348.`

## Javascript

 `// This function generates 'x' with probability px/100, 'y' with ` `// probability py/100  and 'z' with probability pz/100:` `// Assumption: px + py + pz = 100 where px, py and pz lie ` `// between 0 to 100 ` `function` `random(x, y, z, px, py, pz)` `{       ` `        ``// Generate a number from 1 to 100` `        ``let r = Math.floor(Math.random() * 100) + 1;` `     `  `        ``// r is smaller than px with probability px/100` `        ``if` `(r <= px)` `            ``return` `x;`   `         ``// r is greater than px and smaller than or equal to px+py ` `         ``// with probability py/100 ` `        ``if` `(r <= (px+py))` `            ``return` `y;`   `         ``// r is greater than px+py and smaller than or equal to 100 ` `         ``// with probability pz/100 ` `        ``else` `            ``return` `z;` `}`   `// This code is contributed by subhammahato348.`

Time Complexity: O(1)

Auxiliary Space: O(1)

This function will solve the purpose of generating 3 numbers with given three probabilities.