Amazon used to ask this problem as part of their interview:

A drawer contains 12 identical black socks and 12 identical white socks. If you pick 2 socks at random, what is the probability of getting a matching pair?

Think about it for a few minutes before scrolling down to read this further.

Ready?

My immediate reaction was “11/23”. But the question is supposed to be hard, which is why I assumed my answer was completely wrong. Well, maybe it wasn’t? There is only one way to verify.

It takes less than a second to do this experiment a million times in a row. So let’s do that.

Apparently, the most common wrong answer is 50%.

Let’s start. Here is our drawer filled with socks.

const drawer = [
    '⚪️', '⚪️', '⚪️', '⚪️', '⚪️', '⚪️',
    '⚪️', '⚪️', '⚪️', '⚪️', '⚪️', '⚪️',
    '⚫️', '⚫️', '⚫️', '⚫️', '⚫️', '⚫️',
    '⚫️', '⚫️', '⚫️', '⚫️', '⚫️', '⚫️',
]

We have exactly 12 white and 12 black socks in our array. Now, we need to randomly draw two socks from here.

const getRandomInt = max => Math.floor(Math.random() * max)

This function will return a random integer less than the max value it takes in. Note that max is non-inclusive so we can pass in the array length. In JavaScript, array indexing starts at 0, so for an array with 24 elements, the indexes range from 0 to 23.

We can use our function to draw two socks.

const firstDrawIndex = getRandomInt(24)
const [firstSock] = drawer.splice(firstDrawIndex, 1)

const secondDrawIndex = getRandomInt(23)
const [secondSock] = drawer.splice(secondDrawIndex, 1)

return firstSock === secondSock

splice will remove the sock from the array and return the resulting item that was just removed from the array. It will return an array with a single item, so we just need to pick the first element.

We have a pair now. Let’s just check if these two socks are the same color.

firstSock === secondSock

Whenever they are equal, we have a matching pair. Whenever they’re not, we have a non-matching pair.

Let’s move the logic we have so far into a function drawPair and run it a million times.

And let’s keep counting the result while doing that.

let matchingCount = 0
let nonMatchingCount = 0

for (let i = 0; i < 1000000; i++) {
    drawPair() ? matchingCount++ : nonMatchingCount++
}

const probability = Number(
  matchingCount / (matchingCount + nonMatchingCount) * 100)
  + '%'

Have fun:

We should be getting results around %47.8, which is 11/23. Here is the actual number in a higher precision:

(11/23) * 100 = 47.82608695652174%