Add comments explaining how num is calculated as a random integer between minimum and maximum.

Author: HoussamLh

Sprint-1/1-key-exercises/4-random.js

@@ -3,7 +3,74 @@ const maximum = 100;
 
 const num = Math.floor(Math.random() * (maximum - minimum + 1)) + minimum;
 
-// In this exercise, you will need to work out what num represents?
-// Try breaking down the expression and using documentation to explain what it means
-// It will help to think about the order in which expressions are evaluated
-// Try logging the value of num and running the program several times to build an idea of what the program is doing
+// 1- In this exercise, you will need to work out what num represents?
+
+// the num gives a random whole number between 1 and 100 like 73, 12, or 100.
+
+// 2- Try breaking down the expression and using documentation to explain what it means
+/*
+
+1. Math.random()
+
+Returns a random decimal number between 0 and 1 but never gives 1.0.
+
+Example: 0.24 
+
+2. (maximum - minimum + 1)
+
+This gives number of possible values.
+
+Without the +1, we'd only get the difference, not the full count.
+
+for example:
+
+5 - 1 = 4 → but there are actually 5 numbers: 1, 2, 3, 4, 5
+
+So we add +1 to include both ends of the range.
+
+3. Math.random() * (maximum - minimum + 1)
+
+This gives a random decimal number between 0 and 100 (like 24, 65 ...)
+
+Because we want the random decimal scaled to the size of the range of possible values.
+
+For example, if we want a number between 1 and 100 (inclusive), there are 100 possible numbers (1, 2, ..., 100).
+
+Multiplying by 100 means the decimal is scaled up to cover all those possibilities before rounding.
+
+4. Math.floor(...)
+
+This rounds the decimal down to the nearest whole number.
+
+Example: Math.floor(78.43) → 78
+
+5. + minimum
+
+we add the minimum to shift the range correctly, and make sure the random number up to start from minimum.
+
+5-1- for example if we remove the + minimum 
+
+5-1-1 Math.random() 0.9999 * 99 + 1 → only goes up to 99.999... → max = 99.999... → floor = 100 (but very unlikely) 
+
+now 100 becomes very hard to reach, and in many cases, you never get it.
+
+5-1-2 Math.random() 0.00 * 99 + 1 → only goes up to 0... → max = 0... → floor = 0 (now the minimum is 0, and can appears) 
+
+conclusion : when we don’t add + minimum, there is a chance that 1 appears, but it’s not the guaranteed minimum anymore — 
+
+and the range starts at 0, not 1.
+
+5-2- when we add +minimum 
+
+now we make sure the min and max can appear in the final results and make sure the minimum is 1 not 0. 
+
+Minimum appears when random = 0
+
+Maximum appears when random is almost 1 (like 0.9999...).
+
+example : Math.random() * 99 + 1 → up to 0.99 → max = 99 → floor = 99 → +1 = 100 (so more possibilities for 100 to appears) 
+
+*/
+
+//It will help to think about the order in which expressions are evaluated
+//Try logging the value of num and running the program several times to build an idea of what the program is doing