4. Probability
Basic Concepts of Probability
1:40 minutesProblem 4.1.3a
Textbook Question
Dice and Coins
a. Find the probability that when a single six-sided die is rolled, the outcome is 5.
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability of rolling a 5 on a single six-sided die. A six-sided die has six equally likely outcomes: {1, 2, 3, 4, 5, 6}.
Step 2: Recall the formula for probability. The probability of an event occurring is given by: .
Step 3: Identify the favorable outcomes. In this case, the favorable outcome is rolling a 5, which is just one specific outcome.
Step 4: Identify the total number of possible outcomes. Since the die has six sides, there are 6 possible outcomes in total.
Step 5: Substitute the values into the probability formula. Using the formula from Step 2, substitute the number of favorable outcomes (1) and the total number of possible outcomes (6) to calculate the probability.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. An event with a probability of 0 means it cannot happen, while a probability of 1 means it is certain to happen. In the context of rolling a die, the probability of rolling a specific number is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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Sample Space
The sample space is the set of all possible outcomes of a random experiment. For a single six-sided die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is crucial for calculating probabilities, as it provides the total number of outcomes against which favorable outcomes are compared.
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Favorable Outcomes
Favorable outcomes refer to the specific results of an experiment that satisfy the condition of interest. In the case of rolling a die and wanting to find the probability of rolling a 5, there is only one favorable outcome (rolling a 5) out of the six possible outcomes. This concept is essential for determining the probability by identifying how many outcomes meet the criteria of the event.
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