You choose one of two identical looking bags at random. One bag has three black marbles and one white marble. The other has three white marbles and one black marble.

After choosing a bag you draw one marble out at random. You notice it is black. You then put it back and draw another marble out of the same bag at random.

What is the probability that the second marble drawn is black?

Now i know this isnt the way you wanted it solved, but I ran a simulation and this is the result I got bored. 

EDIT!!!  I originally compiled the wrong program, this is the Correct result.

% chance                        trial

.6250167304391642           1016112
.6250161153336292           1016113
.6250161153336292           1016113
.6250161153336292           1016113
.6250161153336292           1016113
.6250164843708481           1016114
.6250168534073407           1016115
.6250168534073407           1016115
.6250172224431069           1016116
.6250175914781467           1016117
.6250169763747911           1016118
.6250163612726463           1016119
.625016730307444            1016120
.6250170993415154           1016121
.6250170993415154           1016121
.6250164842410656           1016122
.6250164842410656           1016122
.6250158691418264           1016123
.6250158691418264           1016123
.6250162381756558           1016124
.6250166072087587           1016125
.6250166072087587           1016125
.6250166072087587           1016125

Edited on September 15, 2004, 10:28 pm

Posted by gabbo on 2004-09-15 22:11:19