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Rolling the Dice If three dice are rolled, find the probability of getting a sum of 6.

$\dfrac{10}{216}$

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 5

Sampling and Data

Probability Topics

Temple University

Piedmont College

Cairn University

Lectures

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01:01

What is the probability of…

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Two dice are rolled. Find …

01:07

Rolling a Die A die is rol…

00:38

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In $3-5,$ find exact proba…

now we have three dies and we wrote them. And we want to know what is the probability that the three dies. Add up to six, and first let let's give names to the three days and call them A B and C, and we know that each dice could be 1 to 6, right? And the three of them they're independent. So the number of all the possible combinations we can have is six times six times six, right? And it ISS six cube. This he calls 216. Now, the next thing we care about is how maney combinations. We can have that add up to six. Right? So I think the easiest way here is to list all the possible combinations. Um, but we have to be very careful because there are a lot of combinations. So now let's try toe list. Um, now, um, we want the the day I say to be one, and that s B still one c is for now. We fixed the value of a and at one on B and see, of course, it's three. Fix A and still at wannabe, it's 132 right, and we do this again. It's then we get one for one. Now, if we fix the value of a we cannot have other. Any other choices? Right. So now next, we will have a B two and baby one and C B three fix the value of a and at one on B, we get to to To and again at one on B. We got 231 Um, if we fix the value of a can we have any other possible choices? No, because if we still want to be and this, then the dicey would be zero. So next week, Um, that a two b three Andi B b one C B two, three to one. Right. And that's all for three. Um So next we start with four. Andi, the only choice is 11 We cannot have any other possible choice. Um, can we have five on dice? A. No, we can't because we don't have zero on a days. Right? And we can have six Sunday, I say so. These are all the possible combinations that can add up to six. And let's count how many? How many of them? 1234 Now That's mark them. One, 23456 789 10. So there are 10 of them that add up to six. So finally, the probability off three. Nice and up. Um, and up to six equals 10. Divided by all the possible combinations, which is 216. Sorry. And this goes to 0.0, 46 and we're done.

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