How do you find the probability of a pair of dice?
Video transcriptFind the probability of rolling doubles on two six-sided dice numbered from 1 to 6. So when they're talking about rolling doubles, they're just saying, if I roll the two dice, I get the same number on the top of both. So, for example, a 1 and a 1, that's doubles. A 2 and a 2, that is doubles. A 3 and a 3, a 4 and a 4, a 5 and a 5, a 6 and a 6, all of those are instances of doubles. So the event in question is rolling doubles on two six-sided dice numbered from 1 to 6. So let's think about all of the possible outcomes. Or another way to think about it, let's think about the sample space here. So what can we roll on the first die. So let me write this as die number 1. What are the possible rolls? Well, they're numbered from 1 to 6. It's a six-sided die, so I can get a 1, a 2, a 3, a 4, a 5, or a 6. Now let's think about the second die, so die number 2. Well, exact same thing. I could get a 1, a 2, a 3, a 4, a 5, or a 6. Now, given these possible outcomes for each of the die, we can now think of the outcomes for both die. So, for example, in this-- let me draw a grid here just to make it a little bit neater. So let me draw a line there and then a line right over there. Let me draw actually several of these, just so that we could really do this a little bit clearer. So let me draw a full grid. All right. And then let me draw the vertical lines, only a few more left. There we go. Now, all of this top row, these are the outcomes where I roll a 1 on the first die. So I roll a 1 on the first die. These are all of those outcomes. And this would be I run a 1 on the second die, but I'll fill that in later. These are all of the outcomes where I roll a 2 on the first die. This is where I roll a 3 on the first die. 4-- I think you get the idea-- on the first die. And then a 5 on the first to die. And then finally, this last row is all the outcomes where I roll a 6 on the first die. Now, we can go through the columns, and this first column is where we roll a 1 on the second die. This is where we roll a 2 on the second die. So let's draw that out, write it out, and fill in the chart. Here's where we roll a 3 on the second die. This is a comma that I'm doing between the two numbers. Here is where we have a 4. And then here is where we roll a 5 on the second die, just filling this in. This last column is where we roll a 6 on the second die. Now, every one of these represents a possible outcome. This outcome is where we roll a 1 on the first die and a 1 on the second die. This outcome is where we roll a 3 on the first die, a 2 on the second die. This outcome is where we roll a 4 on the first die and a 5 on the second die. And you can see here, there are 36 possible outcomes, 6 times 6 possible outcomes. Now, with this out of the way, how many of these outcomes satisfy our criteria of rolling doubles on two six-sided dice? How many of these outcomes are essentially described by our event? Well, we see them right here. Doubles, well, that's rolling a 1 and 1, that's a 2 and a 2, a 3 and a 3, a 4 and a 4, a 5 and a 5, and a 6 and a 6. So we have 1, 2, 3, 4, 5, 6 events satisfy this event, or are the outcomes that are consistent with this event. Now given that, let's answer our question. What is the probability of rolling doubles on two six-sided die numbered from 1 to 6? Well, the probability is going to be equal to the number of outcomes that satisfy our criteria, or the number of outcomes for this event, which are 6-- we just figured that out-- over the total-- I want to do that pink color-- number of outcomes, over the size of our sample space. So this right over here, we have 36 total outcomes. So we have 36 outcomes, and if you simplify this, 6/36 is the same thing as 1/6. So the probability of rolling doubles on two six-sided dice numbered from 1 to 6 is 1/6. Show
What are the most likely outcomes from rolling a pair of dice?Assuming we have a standard six-sided die, the odds of rolling a particular value are 1/6. There is an equal probability of rolling each of the numbers 1-6. But, when we have two dice, the odds are not as simple. For example, there's only one way to roll a two (snake eyes), but there's a lot of ways to roll a seven (1+6, 2+5, 3+4). Let's count how many ways there are to get each value, 2 through 12:
If we want to calculate the probability of rolling, say, a five, we need to divide the number of ways to get 5 by the total possible combinations of two dice. How many total combinations are possible from rolling two dice? Since each die has 6 values, there are \(6*6=36\) total combinations we could get. If you add up the numbers in the total column above, you'll get 36. So, we can calculate the probabilities of each outcome:
Related Pages
How do you find the probability of two dice?Total Score from Two or More Dice
If an individual wants to know the likelihood of getting a particular total sore by rolling two or more dice, then one must go back to the simple rule. This simple rule is probability= number of desired outcomes divided by the number of possible outcomes.
What is the probability of a pair of dice?If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.
How many possibilities are there with 2 dice?When two dice are rolled, there are now 36 different and unique ways the dice can come up. This figure is arrived at by multiplying the number of ways the first die can come up (six) by the number of ways the second die can come up (six). 6 x 6 = 36.
What is the probability of rolling a pair with 2 dice?The number of different outcomes on two dice is the number of different outcomes on the first die (6) TIMES the number of different outcomes on the second (6), or 36. The probability of rolling doubles is 1/6, because there are 6 ways to roll doubles. 6/36 = 36.
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