## If A Fair 6-Sided Die Is Rolled Three Times, What Is The Probability That Exactly One 3 Is Rolled?

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## Answers ( 2 )

## If A Fair 6-Sided Die Is Rolled Three Times, What Is The Probability That Exactly One 3 Is Rolled?

## Introduction

We can all agree that understanding the probability of something occurring is an important part of life. Whether it’s the chance of winning a game, landing a job, or even just predicting the weather, it’s always good to have a basic understanding of what could happen. That’s especially true when it comes to rolling dice. Knowing how to calculate the chances of certain numbers being rolled on a fair die is essential for any gambler or games enthusiast. But what if you want to know the odds of only one specific number being rolled out of three tries? Well, this blog post will explain exactly that — if a fair six-sided die is rolled three times, what is the probability that exactly one 3 is rolled? Read on to find out!

## The Probability Formula

If a fair-sided die is rolled three times, the probability that exactly one is rolled is 1/3. This is because there are three possible outcomes when rolling a die (1, 2, 3), and only one of those outcomes results in exactly one being rolled. Therefore, the probability formula for this scenario is 1/3.

## The Die Is Rolled Three Times

A fair-sided die is rolled three times. The probability that exactly one is rolled is 1/6 * 1/6 * 5/6 = 25/216.

## Conclusion

It is clear that when rolling a fair 6-sided die three times, the probability of exactly one 3 being rolled is 0.25 or 25%. This means that there is a 25% chance of getting one 3 if the die is rolled three times. Therefore it can be concluded that this probability falls in line with expectations and demonstrates how probabilities can be calculated when rolling dice multiple times.

Rolling dice can be fun, but it can also be confusing when trying to figure out the probability of what might happen. Take for example, the classic six-sided die and the probability of rolling exactly one 3 when it is rolled three times.

Before we get into the probability of rolling exactly one 3, let’s first take a look at the basics of probability. Probability is the measure of how likely something is to happen, with a probability of 1 being certain and a probability of 0 being impossible.

When it comes to rolling a six-sided die three times, there are six possible outcomes, so the probability of rolling a 3 is 1/6. That means that the probability of rolling exactly one 3 is 1/6 x 1/6 x 5/6 = 25/216.

But what if you want to know the probability of rolling exactly two 3s? Well, in this case, you can use the same calculation, but with different numbers. The probability of rolling two 3s would be 1/6 x 1/6 x 1/6 = 1/216.

Now that we’ve looked at the probability of rolling one or two 3s, let’s move on to the probability of rolling exactly one 3 when the die is rolled three times.

The probability of rolling exactly one 3 is 1/6 x 5/6 x 5/6 = 125/216. That means that there is a 57.87% chance that exactly one 3 will be rolled when the die is rolled three times.

So, if you’re ever feeling adventurous and decide to roll a six-sided die three times, there’s a good chance that you’ll get exactly one 3!