Calculate the probabilities, when you throw two dice, of obtaining

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. What I've shown here is all the different ways that you can get the same sum when rolling two dice. So, in blue is the sum, and in black is the number that shows up on each of the die. The first die could be a number of four, say, and then the other die could be a number three. And the four and the three meet here at seven. So four and three makes seven. Or one die could be a six, the other one could be a two, and then six and a two meet at eight. So there are a total of 36 numbers in blue. So there are 36 different possibilities, 36 different microstates. If we calculate the probability of getting a four, that's one macrostate four. And there are three different ways that you can get a total of four. So there are three microstates, added up to a total of 36 microstates corresponding to a four total. And that's 8.3 percent. And for getting a total of 10, there are three microstates corresponding to that as well. And so 8.3 percent is the probability of rolling a 10 too.