Question

(Dice Rolling) Write a program that simulates the rolling of two dice. The program should use rand to roll the first die and should use rand again to roll the second die. The sum of the two values should then be calculated. [Note: Each die can show an integer value from 1 to 6, so the sum of the two values will vary from 2 to \(12,\) with 7 being the most frequent sum and 2 and 12 being the least frequent sums.] Figure 7.26 shows the 36 possible combinations of the two dice. Your program should roll the two dice 36,000 times. Use a one-dimensional array to tally the numbers of times each possible sum appears. Print the results in a tabular format. Also, determine if the totals are reasonable (i.e., there are six ways to roll a \(7,\) so approximately one-sixth of all the rolls should be 7 ).

Short answer

Initialize an array to count each sum frequency when rolling two dice 36,000 times, and print the result in a table. Sum 7 should appear approximately 6,000 times, being one-sixth of all rolls.

Step-by-step solution

Initialize the Program

Start by including necessary headers such as and , as well as to seed the random number generator. Initialize constants for the number of sides on a die (6), the number of rolls (36000), and the array size for tallies (13) since the possible sums range from 2 to 12.

Seed the Random Number Generator

Call srand(time(NULL)) to seed the random number generator with the current time, ensuring that you get different results every time the program is run.

Initialize the Tally Array

Declare an array to keep track of the sum frequencies and initialize all its elements to 0.

Simulate Rolling the Dice

Use a for loop to roll the dice 36,000 times. Inside the loop, generate two random numbers each between 1 and 6 representing the dice rolls, calculate their sum, and increment the corresponding index in the tally array.

Print the Results in a Tabular Format

After rolling the dice 36,000 times, print the outcomes. Use another for loop to iterate through the tally array starting from index 2 to 12, and print the index along with the frequency of each sum.

Analyze the Frequency of Sum 7

To verify if the totals are reasonable, compare the frequency of the sum of 7 against the theoretical expectation. Since there are 6 ways to roll a 7 out of 36 possible combinations, the frequency of 7 should be around one-sixth of the total rolls.

Key concepts

Random Number Generation in C++

Random number generation is a fundamental aspect of many programs, including games, simulations, and even security algorithms. A C++ Dice Rolling Program, as described in our problem, relies on generating random numbers to simulate the roll of dice.

The C++ standard library offers the rand() function, which returns a pseudo-random number within a specified range. In the context of rolling dice, this range is typically between 1 and 6 to represent a die's faces. To get a seemingly random set of values on each program run, we need to seed the random number generator, which is typically done using the current time with the expression srand(time(NULL)). This process initializes the random number generator with a starting point for its sequence, ensuring non-repetitive and unpredictable sequences of numbers every time the program is executed.

However, it's important to note that the rand() function generates pseudo-random numbers based on a deterministic algorithm. For most college-level projects and simulations, this is sufficiently unpredictable. Advanced applications requiring high levels of randomness might need more sophisticated methods.

Control Structures in C++

Control structures are at the heart of programming languages, allowing for the execution of code blocks based on conditions or repeatedly running a section of code. In C++, common control structures include loops (like for, while, do-while) and conditional statements like if, else, and switch.

In the Dice Rolling Program, a for loop facilitates the simulation of dice rolls 36,000 times. The choice of a for loop here is due to its compact structure, which is ideal for executing a code block a known number of times. It is initialized with a counter, a condition to continue looping, and an increment action.

Inside the loop, the dice are 'rolled' by generating random numbers. Afterward, the sum is calculated and tallied. By understanding and properly using control structures, programmers can create efficient and easily understandable code that performs repetitive tasks effortlessly and manages flow control judiciously.

Arrays in C++

Arrays are one of the simplest and most useful data structures in C++. They allow for the storage of multiple items of the same data type in a contiguous block of memory. In the context of our Dice Rolling Program, an array keeps a tally of how frequently each possible dice sum appears during the 36,000 rolls.

To accurately record the roll outcomes, we declare a one-dimensional array with enough elements to represent each possible sum, which for two six-sided dice ranges from 2 to 12, thus requiring 11 elements. Since arrays in C++ are zero-indexed, we often use an array size of 13 and start iterating from index 2 for convenience.

The initialization of array elements to zero is crucial to avoid any garbage values, as C++ does not automatically initialize array elements. After rolling the dice, each sum's frequency is updated by incrementing the value at the array index corresponding to the sum. Arrays, with their fixed size and direct index access, prove to be an efficient way to handle this type of data aggregation.

Understanding arrays and their usage in C++ is essential, as they form the base for more complex data structures and are widely used in various applications to organize and process data systematically.