Lesson 4.4
Understanding Compound events
Lesson objectives
- Identify the outcomes of everyday events.
- Identify the probability of a compound event
Independent Compound events
Independent Compound Probability- The probability of two independent events occurring together. Independent Events- Events that are not dependent upon or impacted by another event.
Example of Independent Events- Rolling a die and flipping a coin... the number rolled on the die has no impact on whether the coin flip lands on heads or tails!
Exploration
Let's stick with our die roll and coin flip example. We can show the possible outcomes of each independent event in multiple ways including written lists, tree diagrams, and tables.
Outcomes: heads, tails
Outcomes: 1, 2, 3, 4, 5, 6
Click to relate these outcomes to probability!
There are TWO outcomes to flipping a standard coin!
There are SIX outcomes to rolling a standard die!
Exploration
We can show the possible outcomes of the compound event in multiple ways as well!.
Outcomes: 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T
Click to relate these outcomes to probability!
There are TWELVE outcomes to the compound event of rolling a standard die and flipping a standard coin!
The Shortcut!
Creating tables, tree diagrams, and lists to determine total outcomes becomes impractical with events that have a large number of outcomes. Thankfully, there is a shortcut.
The compound probability of two independent events can be calculated by multiplying the probability of the first event, by the probability of the second event.
Let's continue with our example... The probability of rolling a four AND flipping heads could be expressed as: P(four, heads) = P(four) P(heads)
How did we get1/6 and 1/12?
Try it!
Jackson is playing a game at the carnival. He must spin the spinner shown to the right twice to play the game. Jackson wins if he lands on a yellow space on both spins.
Try it!
Lucia's family is ordering pizza. The pizza shop is offering a special deal for Pizza Pizzazz Friday. Orders are 50% off, but what you get is a surprise. There are three types of crust and seven toppings.
Try it!
As a reminder, for Pizza Pizzazz Friday, orders are 50% off, but what you get is a surprise. There are three types of crust and seven toppings.
Probability Review
The probability of rolling a four on a standard die or P(four) is 1/6 because there is 1 four (favorable outcome) and 6 sides (total outcomes). The probability of flipping heads or P(heads) on a standard coin is 1/2 because there is 1 heads side (favorable outcome) and 2 sides (total outcomes).
Probability of Compound Events
The probability of any of these compound events, four and heads for example, is 1/12. There is 1 outcome in which you would roll a four AND flip heads. There are 12 total outcomes!
Probability Review
The probability of rolling any number, for example a four, on a standard die is 1/6 because there is 1 four (favorable outcome) and 6 sides (total outcomes). The probability of flipping either side, for example heads, on a standard coin is 1/2 because there is 1 heads side (favorable outcome) and 2 sides (total outcomes).
4.4 Math 7 Understanding Compound Events
Amy Gilga
Created on June 25, 2024
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Transcript
Lesson 4.4
Understanding Compound events
Lesson objectives
Independent Compound events
Independent Compound Probability- The probability of two independent events occurring together. Independent Events- Events that are not dependent upon or impacted by another event.
Example of Independent Events- Rolling a die and flipping a coin... the number rolled on the die has no impact on whether the coin flip lands on heads or tails!
Exploration
Let's stick with our die roll and coin flip example. We can show the possible outcomes of each independent event in multiple ways including written lists, tree diagrams, and tables.
Outcomes: heads, tails
Outcomes: 1, 2, 3, 4, 5, 6
Click to relate these outcomes to probability!
There are TWO outcomes to flipping a standard coin!
There are SIX outcomes to rolling a standard die!
Exploration
We can show the possible outcomes of the compound event in multiple ways as well!.
Outcomes: 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T
Click to relate these outcomes to probability!
There are TWELVE outcomes to the compound event of rolling a standard die and flipping a standard coin!
The Shortcut!
Creating tables, tree diagrams, and lists to determine total outcomes becomes impractical with events that have a large number of outcomes. Thankfully, there is a shortcut.
The compound probability of two independent events can be calculated by multiplying the probability of the first event, by the probability of the second event.
Let's continue with our example... The probability of rolling a four AND flipping heads could be expressed as: P(four, heads) = P(four) P(heads)
How did we get1/6 and 1/12?
Try it!
Jackson is playing a game at the carnival. He must spin the spinner shown to the right twice to play the game. Jackson wins if he lands on a yellow space on both spins.
Try it!
Lucia's family is ordering pizza. The pizza shop is offering a special deal for Pizza Pizzazz Friday. Orders are 50% off, but what you get is a surprise. There are three types of crust and seven toppings.
Try it!
As a reminder, for Pizza Pizzazz Friday, orders are 50% off, but what you get is a surprise. There are three types of crust and seven toppings.
Probability Review
The probability of rolling a four on a standard die or P(four) is 1/6 because there is 1 four (favorable outcome) and 6 sides (total outcomes). The probability of flipping heads or P(heads) on a standard coin is 1/2 because there is 1 heads side (favorable outcome) and 2 sides (total outcomes).
Probability of Compound Events
The probability of any of these compound events, four and heads for example, is 1/12. There is 1 outcome in which you would roll a four AND flip heads. There are 12 total outcomes!
Probability Review
The probability of rolling any number, for example a four, on a standard die is 1/6 because there is 1 four (favorable outcome) and 6 sides (total outcomes). The probability of flipping either side, for example heads, on a standard coin is 1/2 because there is 1 heads side (favorable outcome) and 2 sides (total outcomes).