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1. Two standard dice (faces 1 to 6) are rolled. How many of the 36 equally likely outcomes give a total of 7?

Type a number.

2. What does this program print? It counts the ways for two dice with 4 faces and keeps the totals 0 to 5. ``

cpp
#include <iostream>
#include <utility>
#include <vector>

int main() {
    std::vector<int> prev(6, 0);
    prev[0] = 1;
    for (int i = 1; i <= 2; ++i) {
        std::vector<int> curr(6, 0);
        for (int s = 0; s <= 5; ++s) {
            for (int f = 1; f <= 4 && f <= s; ++f) {
                curr[s] += prev[s - f];
            }
        }
        prev = std::move(curr);
    }
    std::cout << prev[5] << ' ' << prev[2] << '\n';
}

``

4 23 14 11 4

3. How many equally likely outcomes are there when three dice with 6 faces are rolled?

Type a number.

4. The lesson says 6 / 36 gives 0 when both numbers are integers. Why must a probability never be made by dividing two integer counts?

The result is always negative when the counts are unsignedInteger division rounds down, so 6 / 36 becomes 0 instead of 1/6The number 36 does not fit in a std::uint64_tThe compiler refuses to divide two unsigned integers

5. What does this program print? ``

cpp
#include <cstdint>
#include <iostream>

int main() {
    std::uint64_t ways = 6;
    std::uint64_t outcomes = 36;
    std::cout << ways / outcomes << ' ' << (ways * 6) / outcomes << '\n';
}

``

0 11 10 00 6

Dice probability