Puzzler of 02/18/2012: use Bayes' theorem: P(A|B) = P(B|A) * P(A) / P(B)

The Show
21

littlemouse. I suggest you run a simulation and see for yourself.
we can argue for many days about the theory, but perhaps a little empirical evidence will help you.
Here. I’ll make it easy. Here’s a C program to guide you.
card 0 = green/green
card 1 = red/green
card 2 = red/red

#include “stdio.h”
#include “stdlib.h”

#define VM_RANDOM_INT(a,b)
((int)((a)+((b)-(a)+1)*((double)rand()/((double)RAND_MAX+1))))

int
main(int argc, char **argv)
{
int ii, nLoop = atoi(argv[1]);
int nRed = 0, nRedRed = 0;
// nRed means there is red on at least one side of the card

for (ii = 0; ii < nLoop; ii++) {
    int card = VM_RANDOM_INT(0, 2);
    int side = VM_RANDOM_INT(0, 1);
    if (card) {
        nRed++;
        if (side) {
            nRedRed++;
        }
    }
}

printf("%d = nRed = %g %%

“, nRed, (double)nRed / nLoop);
printf(”%d = nRedRed = %g %%
", nRedRed, (double)nRedRed / nLoop);
}