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Today, we're diving into simple events in probability. To begin with, does anyone know what a simple event is?
Is it when there's only one outcome possible?
Exactly! A simple event consists of a single outcome from a sample space. Can someone give an example?
Like rolling a die and getting a 3?
Perfect! What about the total possibilities when rolling a die?
Six possibilities: 1, 2, 3, 4, 5, and 6.
Exactly. Each number is a simple event. Now, let’s look into calculating their probabilities.
To calculate the probability of a simple event, we use the formula: P(E) = Number of favorable outcomes / Total number of outcomes. Can anyone tell me what the favorable outcomes might be when rolling a die to get a number greater than 4?
It would be 5 and 6, so that's 2 favorable outcomes.
Correct! And the total outcomes when rolling a die?
There are 6 total outcomes.
Great! So plugging these into our formula, what’s the probability?
P(number > 4) is 2 over 6, which simplifies to 1 over 3.
Absolutely right! This practice is essential when approaching more complex events.
Now let's relate this to real life. Can someone give me a simple event they might encounter?
Tossing a coin and getting heads!
Great example! So, if we toss a coin, what are the total outcomes?
Two outcomes: heads or tails.
Exactly! What's the probability of getting heads?
That would be 1 out of 2, or 50 percent!
Yes! Connecting these concepts to everyday activities makes understanding probability much easier.
To wrap up, can someone summarize what we learned about simple events?
We learned that simple events have just one outcome and how to calculate their probabilities.
Exactly! Now, let’s try a quick practice problem: What is the probability of rolling an even number on a die?
The even numbers are 2, 4, and 6, so that's 3 favorable outcomes.
And the total outcomes are still 6, so the probability is 3 over 6, or 1 over 2.
Well done! Remember these steps, as they will help us in more complex scenarios in the future.
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In this section, students learn about simple events, defined as events comprised of a single outcome from a sample space. The section provides examples and calculations to find the probability of such events.
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Simple events involve only one outcome from the sample space.
A simple event is defined as an event that consists of a single outcome. In probability theory, an outcome is a specific result of an experiment. For example, if we roll a die, the possible outcomes are 1, 2, 3, 4, 5, and 6. Each of these results can be considered a simple event because each represents just one specific potential outcome of the experiment.
Think of rolling a die as like asking a friend to choose a card from a deck. If you only care about your friend's choice of one specific card, such as the Ace of Spades, you are focused on a single outcome, which makes it a simple event.
Example: Find the probability of getting a number greater than 4 when a die is rolled. Solution: Numbers greater than 4 = {5, 6} → 2 favorable outcomes. Total outcomes = 6. P(number > 4)=26=13P(number > 4) = \frac{2}{6} = \frac{1}{3}
To find the probability of a simple event, we need to determine the number of favorable outcomes and the total number of outcomes from the sample space. In this case, when rolling a die, we want to know the probability of rolling a number greater than 4. The favorable outcomes are 5 and 6, meaning there are 2 outcomes that satisfy our condition. Since there are 6 possible outcomes when rolling a die (1, 2, 3, 4, 5, 6), we calculate the probability as the fraction of favorable outcomes over total outcomes, resulting in P(number > 4) = 2/6, which simplifies to 1/3.
Imagine you are at a carnival game where you need to roll a die. You want to win a prize if you roll over 4. You realize that only two numbers (5 and 6) will win you a prize out of a total of six possibilities. Thus, you have about a 1 in 3 chance of winning with each roll.
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Key Concepts
Simple Event: An event with one outcome from a sample space.
Sample Space: The list of all possible outcomes.
Calculating Probability: P(E) = Number of favorable outcomes / Total number of outcomes.
See how the concepts apply in real-world scenarios to understand their practical implications.
Rolling a die to find the probability of landing on a 4.
Tossing a coin to find the probability of getting tails.
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
Count from one to six, on a die you can mix!
A student named Alex rolls a die and gets excited every time they land on their favorite number, 5. Alex learns that each number is a way to win!
Favorable outcomes over total outcomes: F.O./T.O.
Review key concepts with flashcards.
Term
What is a simple event?
Definition
How do you calculate the probability of a simple event?
What is a sample space?
Review the Definitions for terms.
Term: Simple Event
Definition:
An event that consists of a single outcome from a sample space.
Term: Sample Space
The set of all possible outcomes of an experiment.
Term: Probability
A measure of how likely an event is to occur, ranging from 0 to 1.
Flash Cards
Glossary of Terms