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Chapter 16: Problem 3

What is the probability of getting a 2 on a single throw of a fair die?

Short Answer

Expert verified
The probability of rolling a 2 on a fair die is \( \frac{1}{6} \).

Step by step solution

01

Understanding the Problem

We need to find the probability of rolling a 2 on a fair six-sided die. Each side of the die has an equal chance of landing face up.
02

Identify Total Outcomes

A standard die has 6 faces, representing 6 equally likely outcomes (1, 2, 3, 4, 5, 6). Hence, the total number of possible outcomes when a die is rolled is 6.
03

Identify Favorable Outcomes

The favorable outcome is rolling a 2. Since there is only one face of the die with a 2, there is exactly 1 favorable outcome.
04

Calculate the Probability

Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Thus, the probability of rolling a 2 is given by: \[ P( ext{rolling a 2}) = \frac{1}{6} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Favorable Outcomes
Favorable outcomes in probability refer to the specific results that satisfy the condition you are interested in. Imagine rolling a die and aiming to get a 2. Here, the favorable outcome is rolling a 2. No other number will count for this particular question.
When dealing with dice, each number, from 1 to 6, can appear on a roll. But only one of those numbers is your favorable outcome.
  • Favorable outcomes are what you want to happen鈥攔olling a 2, for example.
  • In our example with a die, there is only 1 favorable side.
  • To identify favorable outcomes, pinpoint the scenarios that directly correspond to the question asked.
Calculating Total Outcomes
Total outcomes encompass all possible results of a given action. With a standard die, you have 6 faces, each representing an outcome when you roll the die: 1, 2, 3, 4, 5, and 6.

These outcomes are crucial for determining probabilities because they form the denominator when calculating the probability of any specific event occurring.
  • Total outcomes include all potential numbers a die can land on.
  • When rolling a fair die, there are always 6 possible results.
  • Remember, without knowing the total outcomes, calculating probability correctly is impossible.
Understanding Dice Probability
Dice probability is a classic example in probability due to its simplicity and clarity. It is the likelihood of rolling a specific number on a fair six-sided die.
To calculate the probability of rolling a specific number, like a 2, divide the number of favorable outcomes (rolling a 2) by the total outcomes (6 numbers). This gives us \( P(\text{rolling a 2}) = \frac{1}{6} \).

  • Probability is a fraction showing how likely something is based on all possible outcomes.
  • It ranges from 0 (impossible event) to 1 (certain event).
  • In dice probability, each number has an equal chance of appearing, which simplifies calculations.

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