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

`// 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;` `}` |

## Python

`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` |

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

This article is contributed by **Harsh Agarwal**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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