<p>Woops – I just scrolled to the end of your question and saw that they want the probabiluty that the marbles are different! I answered for the probability that they are the same. And if you calculate what I gave you, it comes out to 4/9. So the answer is 1- 4/9 (b/c if you subtract out the two ways to have it come out the same, you get left with the prob that it comes out different!)</p>
<p>Still, if I had read it all the way through, I would not use the approach I gave you. Instead:</p>
<p>Think of it as probability of white followed by black + probability of black followed by white:</p>
<p>4/9 x 5/8 + 5/9 x 4/8 </p>
<p>or, since those products are the same, just calculate one of them and then double it (which is what your explanation said to do – but if you don’t understand where the products come from, you are not likely to realize that you can double it…)</p>