Determine Math.random() range or values

Questions on the multiple choice section may be phrased such that they ask you to generate numbers in a given range. See Random numbers on the AP CS A Exam for the technique to approach these.

Other questions start with an existing expression based on Math.random() and ask what range of values can be generated. To answer these questions:

Approach

  1. Start with the range for an unmodified call to Math.random(). This is a double greater than or equal to 0.0 and strictly less than 1.0.

  2. Apply each operation from the expression to the range, one at a time, in the order they are applied in the expression.

Example 1

What range of values can the statement below assign to value?

int value = (int) (Math.random() * 15) + 3;

Step 1: Initial range

int value = Math.random();
// 0.0 <= value < 1.0

Note: The statement does not compile since Math.random() returns a double. That’s ok because this is an intermediate step.

Step 2: After multiplying

int value = Math.random() * 15;
// 0.0 <= value < 15.0

Multiplying 0.0 by 15 results in 0.0. Multiplying 1.0 by 15 results in 15.0.

Note: As in Step 1, this statement does not compile.

Step 3: After casting to an int

int value = (int) (Math.random() * 15);
// 0 <= value <= 14

Casting 0.0 to an int results in 0.

When a number strictly less than (not less than or equal to) 15.0 is cast to an int, the biggest number that can result is 14.

The range could be written as 0 <= value < 15, but it makes more sense to say <= 14 than < 15 for an int.

Note: This statement does compile, though it is not the final statement.

Step 4: After adding

int value = (int) (Math.random() * 15) + 3;
// 3 <= value <= 17

Adding 3 to 0 results in 3. Adding 3 to 14 results in 17.

This is the final range.

Note: This statement compiles and is the final statement.

Example 2

What values can the statement below assign to num?

int num = 4 + (int) (Math.random() * 3);

Step 1: Initial range

int num = Math.random();
// 0.0 <= num < 1.0

Step 2: After multiplying

int num = Math.random() * 3;
// 0.0 <= num < 3.0

Step 3: After casting

int num = (int) (Math.random() * 3);
// 0 <= num <= 2

Step 4: After adding

int num = 4 + (int) (Math.random() * 3);
// 4 <= num <= 6

The statement can assign the values 4, 5, or 6 to num.

Example 3

What range of values can the statement below assign to r?

int r = (int) (Math.random() * 10 + 6);

Step 1: Initial range

int r = Math.random();
// 0.0 <= r < 1.0

Step 2: After multiplying

int r = Math.random() * 10;
// 0.0 <= r < 10.0

Step 3: After adding

int r = Math.random() * 10 + 6;
// 6.0 <= r < 16.0

As discussed above, I don’t like structuring statements that use Math.random() this way. That doesn’t mean I can’t work with code that structures them this way.

Step 4: After casting

int r = (int) (Math.random() * 10 + 6);
// 6 <= r <= 15

This is the final range of values that the statement can assign to r.

Additional resources