/* Example code for finding binomial probabilities in SAS */

OPTIONS pagesize=50 linesize=64; 
/* (setting the page margins) */

/* The command PROBBNML computes _cumulative_ binomial probabilities */

/* To get the cumulative probability, the syntax is: probbnml(p, n, x) */
/* where p, n, and x are values that you fill in */

/* Suppose our random variable X is binomial with n=20 and p=0.65 */

/* Let's answer the following questions */
/* 1. What is the probability of 13 or fewer successes?  P(X <= 13) */
/* 2. What is the probability of 6 or fewer successes? P(X <= 6)  */
/* 3. What is the probability of EXACTLY 13 successes? P(X = 13) */
/* 4. What is the probability of more than 13 successes? P(X > 13) */
/* 5. What is the probability of 13 or more successes? P(X >= 13) */
/* 6. What is the probability of 8, 9, or 10 successes? P(8 <= X <= 10) */

/* This SAS program will give us the answers to all these questions in an instant */
/* I will label the answers to the 6 questions as prob1, prob2, ... , prob6. */

data binom;

prob1 = probbnml(0.65, 20, 13);

prob2 = probbnml(0.65, 20, 6);

prob3 = probbnml(0.65, 20, 13) - probbnml(0.65, 20, 12);

prob4 = 1 - probbnml(0.65, 20, 13);

prob5 = 1 - probbnml(0.65, 20, 12);

prob6 = probbnml(0.65, 20, 10) - probbnml(0.65, 20, 7);

run;

proc print data=binom;
title 'Binomial Probabilities';
run;

/* After we input this program into the program editor and do "Run"->"Submit" */
/* Then the results print in the Output window */

/* Notice how the commands mirror the examples we did in class using the tables */

/* The difference is:  SAS can do these for any n and p, whereas the table only */
/* gives probabilities for certain n and p choices. */