Understanding Probability with a Six-Sided Die

If I roll a fair six-sided die, what is the probability of rolling a number greater than 4?

• A. 1/2
• B. 1/3
• C. 1/6
• D. 2/3

Answer: (B)

To determine the probability of rolling a number greater than 4 on a fair six-sided die, first identify the possible outcomes when rolling the die, which are the numbers 1, 2, 3, 4, 5, and 6. Next, we focus on the favorable outcomes for this specific event, which includes the numbers 5 and 6, as both are greater than 4. Therefore, there are 2 favorable outcomes. The probability is calculated by taking the number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, there are 6 total outcomes (the numbers 1 through 6), so the calculation becomes: Number of favorable outcomes (5, 6) = 2 Total outcomes (1 through 6) = 6 Thus, the probability of rolling a number greater than 4 is: \[ \frac{2}{6} = \frac{1}{3} \] This means that the answer is derived accurately by assessing both the favorable outcomes and the total number of outcomes.

Let’s chat about probability, shall we? It’s not just for math whizzes—it’s everywhere in life. Today, we’re using a straightforward example: rolling a six-sided die. You know how it goes; you roll it, and you want to know what your chances are for getting a number greater than four. So, let’s break this down together.

First up, when you roll that fair six-sided die, you have six possible outcomes: 1, 2, 3, 4, 5, and 6. Picture this: each face of the die is a distinct way to express possibility. But now, here’s the twist—what are our favorable outcomes? We're interested in rolling either a 5 or a 6 because those are the only numbers greater than 4. So, out of those six outcomes, just two (5 and 6) are what we’re looking for.

Now, it’s time for the fun part—calculating the probability! Probability is calculated with a simple formula: it’s all about the number of favorable outcomes divided by the total number of outcomes. In this scenario, we have 2 favorable outcomes (those rolling a 5 and a 6) and 6 total outcomes (the whole range from 1 to 6). When you set it up, it looks like this:

• Number of favorable outcomes: 2 (that’s our 5 and 6)

• Total outcomes: 6 (the 1 through 6 crew)

When you put that into the formula, you get:

[

\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{6} = \frac{1}{3}

]

And voilà! We’ve found that the probability of rolling a number greater than 4 is (\frac{1}{3}). Now, that might feel a bit abstract, but consider it this way: if you rolled that die three times, statistically speaking, you might expect to roll a number greater than 4 once.

Isn’t probability fascinating? It’s like betting on outcomes in life, and just like playing a game, you want to have a good grasp of the odds. Beyond dice, this concept of chance applies everywhere, from card games to predicting weather patterns. It’s all about weighing your options and making informed choices.

So, what’s the takeaway? Understanding how to calculate probability using simple examples, like our die, gives you a solid foundation for tackling more complex problems down the line. The more you practice, the easier it gets. Plus, who doesn’t love a little chance? Now you’re ready to roll with confidence—literally!