Picking Array Values using Probability

Question

I have a homework to do, that is:

Pick a random color, from yellow, blue and red, given the probability of: Yellow: 3/7 Blue: 1/7 Red: 3/7

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I know that I could work this around by using something like: [yellow, yellow, yellow, blue, red, red, red] But I don't think this would be programatically good, since when I chance the probability, I would have to change the array.

So, I thought I could try something like a weight approach

let yellow_probability = 3/7
let blue_probability = 1/7
let red_probability = 3/7
const colors = ['yellow', 'blue', 'red']
function pickPosition(yellow_probability, blue_probability, red_probability){
 let yellow_weight = Math.random() * yellow_probability
 let blue_weight = Math.random() * blue_probability
 let red_weight = Math.random() * red_probability
 let weights = [yellow_weight, blue_weight, red_weight]
 let max_of_array = Math.max.apply(Math, weights);
 pickedColor = weights.indexOf(max_of_array)
 return pickedColor
}
pickedColorIndex = pickPosition(yellow_probability, blue_probability, red_probability)
pickedColor = colors[pickedColorIndex]
console.log(pickedColor)

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I did a test:

let n=1000000; 
let yellow=0, blue=0, red=0; 
for (let i=0; i<n; i++) {
 pickedColorIndex = pickPosition(yellow_probability, blue_probability, red_probability)
 if (pickedColorIndex==0) yellow++
 else if (pickedColorIndex==1) blue++
 else red++;
}
console.log("yellow = " + yellow/n );
console.log("blue = " + blue/n );
console.log("red = " + red/n );

And I would expect this test to output something like:

Yellow = 0.43
Blue = 0.14
Red = 0.43

But I am getting:

Yellow = 0.48
Blue = 0.03
Red = 0.48

It is interesting to point out that the code works when the probabilities are equal (1/3, 1/3, 1/3) or something like (1/2, 1/2, 0)

Can anyone point out what I am doing wrong?

• adiga: Possible duplicate of Generate random integers with probabilities and Javascript Get Random result with probability for specific array
• Victor Maricato: Stackoverflow recommended these posts for me, and the stackoverflow.com/questions/49164635 has a quite similar question to mine, but its answers in general present the apporach I discarded.

Answer 1

Instead of a single random value, you create as many as different items you have and later take the one with the max value.

This promotes values/items with a higher factor/probability.

Instead of this approach, you could take a single random value and take all probabilities into an array and check in which interval the random value is. Take this item.

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EDIT: The code

function getRandomIndex(probabilities) {
 var random = Math.random(),
 i;
 
 for (i = 0; i < probabilities.length; i++) {
 if (random < probabilities[i]) return i;
 random -= probabilities[i];
 }
 return probabilites.length - 1;
}
var probabilities = [3 / 7, 1 / 7, 3 / 7],
 j = 1e6,
 count = [0, 0, 0];
while (j--) count[getRandomIndex(probabilities)]++;
console.log(count);

• briosheje: why not? :P I'm pretty sure no one will complain about that
• Victor Maricato: But, for a single random value, wouldn't I face some problems with equals probabilities? e.g: Yellow and Red have 3/7 probability, so, if I checked the random value on them, it would conflict, wouldn't it?
• Victor Maricato: If you could add some code, it would be helpful to understand your method. Anyway, I will try to implement your method as I understood, by myself.
• Victor Maricato: Not yet, I didn't have access to a computer yet

Answer 2

This is similar to the approach mentioned in the duplicate. You create an array with ratios same as the probabilities. (Here I'm using 2 decimal places and adding ~100 items to the array. You could add multiply by a bigger number and have .toFixed(3) for better accuracy)

function getRandomWithProbability(array) {
 const filled = array.flatMap(([color, prob]) => {
 const length = prob.toFixed(2) * 100;
 return Array.from({ length }).fill(color)
 });
 const random = Math.floor(Math.random() * filled.length);
 return filled[random]
}
const arr = [["yellow", 3/7], ["blue", 1/7], ["red", 3/7]]
console.log(getRandomWithProbability(arr))