3.15 Random Values

Generating Random Numbers

In AP CSP, random values come from RANDOM(a, b), which returns an integer from a through b, including both endpoints. Each possible integer in that range is equally likely, so RANDOM(1, 3) can return 1, 2, or 3.

Random number generation is useful when a program needs behavior that can change from one run to the next, such as a dice roll, a random index, or a simulation event. On the exam, the key skill is usually tracing the possible results of a random expression, not memorizing a specific programming language library.

Here's what the random generator looks like in AP pseudocode: RANDOM(a, b) returns an integer value. RANDOM(a, b) returns a random integer from a to b, inclusive. Example: x <- RANDOM(1,6) can produce 1, 2, 3, 4, 5, or 6.

...and here's its equivalent in Python:

</>Code
import random
c = random.randint(a,b)

Notice how you have to import the random module into your program in order to gain access to the random generator. Note: In AP CSP pseudocode on the Exam Reference Sheet, RANDOM(a, b) is available without any import.

The Python example above will generate a random integer from a to b, inclusive. For example, c = random.randint(0,5) could result in the value of c being 0, 1, 2, 3, 4, or 5. In AP CSP pseudocode, each integer in the range a to b is equally likely to occur. For example, RANDOM(1,3) can return 1, 2, or 3 with equal probability.

Write and evaluate expressions

Use AP pseudocode expressions to produce specific ranges or sets, and list the possible results:

• Die roll: r <- RANDOM(1,6) // results: 1, 2, 3, 4, 5, 6
• Zero-based index: i <- RANDOM(0,9) // results: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Even numbers 0..8: e <- 2 * RANDOM(0,4) // results: 0, 2, 4, 6, 8
• Shifted range: s <- RANDOM(2,7) - 1 // results: 1, 2, 3, 4, 5, 6

Using random number generation in a program means that we might get a different result every time we run the program.

How to Use This on the AP CSP Exam

Random value questions usually ask you to determine every possible result of an expression. First list the outputs of RANDOM(a, b), then apply any arithmetic outside the random call. Remember that both endpoints are included.

Common traps:

• Treating RANDOM(1,6) like it can return 0 or 7. It cannot.
• Forgetting that each integer in the range is equally likely.
• Evaluating only one possible run of the program when the question asks for all possible outputs.
• Mixing up AP pseudocode with Python or JavaScript syntax. The AP Exam Reference Sheet gives you RANDOM(a, b) directly.