Many state lotteries use a variation of the simple lottery portrayed by Listing 7.4. In these variations you choose several numbers from one set and call them the field numbers. For example, you might select five numbers from the field of 1–47).You also pick a single number (called a mega number or a power ball, etc.) from a second range, such as 1–27.To win the grand prize, you have to guess all the picks correctly. The chance of winning is the product of the probability of picking all the field numbers times the probability of picking the mega number. For instance, the probability of winning the example described here is the product of the probability of picking 5 out of 47 correctly times the probability of picking 1 out of 27 correctly. Modify Listing 7.4 to calculate the probability of winning this kind of lottery.

Here’s a sample run of the program in Listing 7.4:
Enter the total number of choices on the game card and
the number of picks allowed:
49 6
You have one chance in 1.39838e+007 of winning.
Next two numbers (q to quit): 51 6
You have one chance in 1.80095e+007 of winning.
Next two numbers (q to quit): 38 6
You have one chance in 2.76068e+006 of winning.
Next two numbers (q to quit): q
bye

Notice that increasing the number of choices on the game card greatly increases the odds against winning.

Transcribed Image Text:

Listing 7.4 lotto.cpp // lotto.cpp -- probability of winning #include // Note: some implementations require double instead of long double long double probability (unsigned numbers, unsigned picks); int main() { using namespace std; double total, choices; cout << "Enter the total number of choices on the game card and\n" "the number of picks allowed: \n"; while ((cin >> total >> choices) && choices <= total) { cout << "You have one chance in "; cout << probability (total, choices); cout << " of winning.\n"; cout << "Next two numbers (q to quit): "; } cout << "bye\n"; return 0; } // the following function calculates the probability of picking picks // numbers correctly from numbers choices long double probability (unsigned numbers, unsigned picks) { // compute the odds. long double result = 1.0; // here come some local variables long double n; unsigned p; for (n numbers, p = picks; p > 0; n--, p--). result result n / p ; return result;