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

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

/* The command PROBHYPR computes _cumulative_ hypergeometric probabilities */

/* To get the cumulative probability, the syntax is: probhypr(N,r,n,x) */
/* where N, S, n, and x are values that you fill in */

/* Suppose our random variable X is hypergeometric with N=12, r=5, and n=4 (like in our class example). */

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

/* This SAS program will give us the answers to all these questions in an instant */
/* I will label the answers to the 5 questions as prob1, prob2, ... , prob5. */

data hyp;
    prob1=probhypr(12,5,4,2) - probhypr(12,5,4,1);   /* P(X = 2) = P(X <= 2) - P(X <= 1) */

    prob2= 1 - probhypr(12,5,4,2);                   /* P(X > 2) = 1 - P(X <= 2) */
 
    prob3=probhypr(12,5,4,1);                        /* P(X < 2) = P(X <= 1) */

    prob4= 1 - probhypr(12,5,4,1);                   /* P(X >= 2) = 1 - P(X <= 1) */

    prob5=probhypr(12,5,4,3) - probhypr(12,5,4,0);   /* P(1 <= X <= 3) = P(X <= 3) - P(X <= 0) */
run;

proc print data=hyp;
title 'Hypergeometric Probabilities';
run;

/* After we input this program into the program editor and run the code */
/* Then the results print in the Output window */