Concept of Math.floor(Math.random() * 5 + 1), what is the true range and why?

Question

By multiplying the random number (which is between 0 and 1) by 5, we make it a random number between 0 and 5 (for example, 3.1841). Math.floor() rounds this number down to a whole number, and adding 1 at the end changes the range from between 0 and 4 to between 1 and 5 (up to and including 5). The explanation above confused me... my interpretation below: --adding the 5 gives it a range of 5 numbers --but it starts with 0 (like an array?) --so it's technically 0 - 4 --and by adding the one, you make it 1 - 5 I am very new to JS, don't even know if this kind of question is appropriate here, but this site has been great so far. Thank you for any help!

Accepted Answer

From the Mozilla Developer Networks' documentation on `Math.random()`:

The Math.random() function returns a floating-point, pseudo-random number in the range [0, 1) that is, from 0 (inclusive) up to but not including 1 (exclusive).

Here are two example randomly generated numbers:

```
Math.random() // 0.011153860716149211
Math.random() // 0.9729151880834252
```

Because of this, when we multiply our randomly generated number by another number, it will range from 0 to a maximum of 1 lower than the number being multiplied by (as `Math.floor()` simply removes the decimal places rather than rounding the number (that is to say, 0.999 becomes 0 when processed with `Math.floor()`, not 1)).

```
Math.floor(0.011153860716149211 * 5) // 0
Math.floor(0.9729151880834252 * 5)   // 4
```

Adding one simply offsets this to the value you're after:

```
Math.floor(0.011153860716149211 * 5) + 1 // 1
Math.floor(0.9729151880834252 * 5) + 1   // 5
```

Concept of Math.floor(Math.random() * 5 + 1), what is the true range and why?

Solution

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