What Is the probability that you draw a purple marble, put it back in dry yellow?

Question

There 12 marbles in a bag, 5 yellow in 7 purple. What is the probability that you draw a purple marble, put it back in the in draw yellow? What What is the probability that you drive purple marble, put it back in then draw a yellow marble? What is The probability of drawing to yellow marbles without replacement?

Answer 1

Since there are 7 purple marbles out of 12 total there is a 7/12 probability you will draw a purple marble on the first draw. The purple marble is replaced restoring the original 12 marbles.

Since there are 5 yellow marbles out of 12 total there is a 5/12 probability you will draw a yellow marble on the second draw

Since each draw when sampling without replacement is independent the probability of drawing a purple marble, replacing it then drawing a yellow marble is 7/12 * 5/12 = 35/144

On the first draw the probability is still 5/12 to draw a yellow marble. Now there are 4 yellow marbles and 11 marbles total, so on the second draw there is a 4/11 probability to draw a yellow marble given you have already drawn a yellow marble and not replacing it.

The probability of drawing two yellow marbles in a row = probability draw yellow marble first time * probability draw yellow marble given you have already drawn one = 5/12 * 4/11 = 20/132 = 5/33