Find the probabilityof rojo doubles on 2 six-sided dicenumbered indigenous 1 to 6. So as soon as they're talkingabout roll doubles, they're just saying,if I role the two dice, I acquire the very same numberon the peak of both. So, for example, a 1and a 1, that's doubles. A 2 and also a 2, that is doubles. A 3 and also a 3, a 4 and also a 4,a 5 and also a 5, a 6 and a 6, all of those areinstances of doubles. So the occasion in questionis rolling doubles on two six-sided dicenumbered from 1 come 6. For this reason let's think around allof the feasible outcomes. Or another means tothink around it, let's think about thesample room here. So what can we rollon the first die. For this reason let me create thisas die number 1. What room the possible rolls? Well, they'renumbered indigenous 1 come 6. It's a six-sided die, so ns canget a 1, a 2, a 3, a 4, a 5, or a 6. Now let's think around thesecond die, so dice number 2. Well, precise same thing. I might get a 1, a 2,a 3, a 4, a 5, or a 6. Now, provided these possibleoutcomes because that each of the die, we can now think of theoutcomes because that both die. So, because that example, in this--let me draw a grid below just to do it a little bit neater. Therefore let me attract a heat there andthen a line right over there. Let me attract actuallyseveral the these, just so the we could reallydo this a tiny bit clearer. For this reason let me attract a complete grid. All right. And then permit me draw thevertical lines, just a couple of more left. There we go. Now, all of this top row,these space the outcomes whereby I roll a 1on the an initial die. So I role a 1 on the very first die. This are all of those outcomes. And also this would certainly be i runa 1 ~ above the second die, however I'll fill that in later. This are every one of theoutcomes whereby I role a 2 ~ above the very first die. This is wherein I rolla 3 ~ above the very first die. 4-- i think you acquire theidea-- ~ above the an initial die. And also then a 5 onthe first to die. And then finally, this lastrow is all the outcomes wherein I role a 6on the first die. Now, we deserve to gothrough the columns, and also this very first column is wherewe roll a 1 on the 2nd die. This is wherein we rolla 2 on the second die. For this reason let's draw that out, writeit out, and fill in the chart. Here's wherein we rolla 3 top top the second die. This is a comma the I'mdoing in between the two numbers. Here is wherein we have a 4. And then right here is wherewe role a 5 top top the 2nd die, simply filling this in. This last column is where weroll a 6 ~ above the second die. Now, every one of theserepresents a feasible outcome. This result is where we rolla 1 ~ above the very first die and a 1 top top the second die. This outcome is wherein weroll a 3 on the very first die, a 2 top top the 2nd die. This result is where weroll a 4 ~ above the first die and also a 5 on the 2nd die. And you deserve to see here, there are36 feasible outcomes, 6 time 6 feasible outcomes. Now, v this out of the way,how plenty of of these outcomes satisfy our criteria the rollingdoubles on two six-sided dice? How plenty of of this outcomesare essentially described by our event? Well, we see them ideal here. Doubles, well, that's rollinga 1 and also 1, that's a 2 and also a 2, a 3 and also a 3, a 4 and a 4, a5 and a 5, and also a 6 and a 6. Therefore we have actually 1, 2, 3, 4, 5, 6events satisfy this event, or are the outcomes the areconsistent with this event. Now provided that, let'sanswer our question. What is the probabilityof rojo doubles on two six-sided dienumbered from 1 to 6? Well, the probabilityis going to be same to the number of outcomesthat accomplish our criteria, or the number of outcomesfor this event, which room 6-- we simply figuredthat out-- over the total-- I desire to do that pinkcolor-- variety of outcomes, over the dimension ofour sample space. For this reason this appropriate over here,we have actually 36 complete outcomes.
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For this reason we have 36 outcomes,and if you leveling this, 6/36 is the same thing as 1/6. For this reason the probabilityof roll doubles on two six-sided dicenumbered from 1 come 6 is 1/6.