Understanding Probability with Dice: Sum of 2 or 9 Explained

When two dice are rolled, what is the probability that the sum is either 2 or 9?

• A. 1/36
• B. 3/36
• C. 5/36
• D. 7/36

Answer: (C)

To determine the probability that the sum of two rolled dice is either 2 or 9, we first need to calculate the total number of possible outcomes when two dice are rolled, which is 6 sides per die multiplied by 6 sides on the other die, resulting in 36 possible combinations. Next, we consider the successful outcomes for each of the sums: For a sum of 2, there is only one combination: (1, 1). Hence, there is 1 successful outcome for this sum. For a sum of 9, multiple combinations yield this result. The successful outcomes are: - (3, 6) - (4, 5) - (5, 4) - (6, 3) This gives us 4 successful outcomes for the sum of 9. Now, we add the successful outcomes for both sums: 1 (for sum = 2) + 4 (for sum = 9) equals 5 successful outcomes. Thus, the probability of rolling a sum of 2 or 9 is the number of successful outcomes (5) divided by the total number of outcomes (36). This leads us to the probability of 5/36. The calculations are hence confirmed by

When it comes to rolling dice, the simplicity of the act can often invite a surprising complexity—especially when we start asking questions about probability. Let's take a look at one such question: What’s the probability of rolling a sum of 2 or 9 when tossing two dice? This might sound a bit daunting at first, but don’t worry; we'll break it down together, step by step.

To start, let's talk about the total possible outcomes when you roll two dice. With each die featuring 6 sides, the math is straightforward: 6 sides on the first die multiplied by 6 sides on the second die gives us a total of 36 different combinations. That’s a whole lot of ways two dice can come together, huh?

Now, focusing in, let’s consider the successful outcomes that can yield a sum of either 2 or 9. For a sum of 2, there’s only one way to achieve this: by rolling (1, 1)—the classic snake eyes. So, we can confidently say there's just 1 successful outcome here.

Now onto the sum of 9. This one’s a little more generous with combinations! We can achieve this sum through the following pairings:

• (3, 6)

• (4, 5)

• (5, 4)

• (6, 3)

If you add those up, that’s 4 successful outcomes for the sum of 9. Now, the suspense builds as we combine our successful outcomes for both sums: we’ve got 1 from the sum of 2 and 4 from the sum of 9. Rounding that out, we arrive at a grand total of 5 successful outcomes.

So, how do we find our probability? Well, it's really as simple as dividing our successful outcomes by the total outcomes we identified earlier. That gives us 5 successful outcomes over 36 total outcomes, leading us to our final probability of 5/36.

Now, why does this matter? Understanding probabilities like this isn’t just fodder for a classroom—it’s foundational knowledge that permeates daily decisions. From games of chance to diverse fields like statistics and finance, a solid grasp of probability can elevate your analytical skills. Plus, it’s kind of fun to think about how likely things are to happen!

In the end, rolling those dice isn’t just a game. It's a gateway into deeper mathematical principles, helping train your mind to navigate the uncertainties of life with a little more confidence. So, the next time you grab a pair of dice, you might just think about the neat little world of probabilities waiting to be discovered!