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A pair of fair dice is rolled. what is the probability of rolling a sum of 8?...

Question

A pair of fair dice is rolled. what is the probability of rolling a sum of 8?

A pair of fair dice is rolled. what is the probability of rolling a sum of 8?



Answers

What is the probability of getting a sum of 8 when a pair of dice are thrown?

Okay, So we want the probability that we rolled doubles Emery World in eight. So we want to see you. What? All can equal eight. So we have six plus two to cost six. We left three plus five. It was five plus three and it will have four plus four. So then we have 345 possibilities here. Surgeon over there will be a five. Then we have one success, so we'll have 1/5.

You have to dice. Each dice has six sides valued one through six, so these two dice to give your together give you a total of six times six or 36 possible outcomes. So let's figure out the probability of rolling two dice that some toe a total of 10 by just figuring out how many combinations give us a total of 10 and divide that by 36. So the combinations that gives a total of 10 are again. We're limited by the fact that our dice can only be the value one through six. So six and four is 14 and six is one and six and four is another one. You also have five and five. Those were the only possible ways you could get to a value of 10. So this is this gives us Ah, 10 36. Excuse me, not 10 36. There are three ways to get to 10 so this gives us 3 36 as our probability, which we could simplify down by dividing by three. So this gives us 1/12 as our probability, Linkenbach said. It is the solution

So we want to know if you roll a set of two dies. What is the probability that the sum of the few dies isn't even number? Well, first we want to know how many possible outcomes do we have when we rolled to dice? Well, for the first dies, we have six options, which is the numbers one through six. And for the second option, we also have six, which is the numbers one through six again and says they are two separate dice. We have that buy the product rule. We have 36 possible pairs, and each of these Paris is equally likely to come out as our outcome. Each of these 36 parishes, Justus likely to be our outcome equally likely to be our outcome. Well, we just need therefore, witches need to show how many of these possible pairs give us an even some. Well, to get even some to get us some where the outcome is even we need to either some to even numbers, or we need to some two out numbers. Well, if you will, the first die and we haven't even number. We have three possible even outcomes, which is 24 and six and then for the second guy is the same thing. And since they're separate dies, we used a product rule and we get that nine out of thes 36 possible pairs are both even and give us, and even some for the odd is the same thing. We have three possible outcomes when we rolled the first dies and these possible outcomes are 13 implied and so are they for the second ice. And similarly, we get nine by the product rule, and we also therefore, we have nine out of these 36 possible pairs give us an even some where both of them are odd numbers. Therefore, the probability that we have the sum off the two dies be uneven. Number is nine plus nine, which is 18 over 36 because the probability that both of them are even he's nine over 36 the probability that both of them are odd is nine over 36. Therefore, the probability that we get uneven pair a pair where the summit's human is 1/2

Okay, So what is the probability that some off the numbers on two dice is even when they are rolled? Okay, So to do this, we have to kind of think, What if the first I comes up like 123 Well, so five and six. Well, if it's 123456 So if you rolled a one on your first die, then you needed to have 123 So you need one and one. You need one and three, and you need one and five for it to be even. So, if you're old too, then you need to to train to we need to and four. And you need two and six and 43 units, three and one and three and three and three and five. So it's pretty easy to see that. For each of these numbers, you'll have 333333 So it would be six chemistry number old favorable outcomes divided by the number of possible outcomes. So each of these so 123456 So this has six possible outcomes. This has sixties, has sixes, have sixes, has six. This is six So if the six some street divided by six times where six. So these 26 cats is out, so that's three divided by six, so that's one over two.


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