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Probability: Compound Events
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What you will learn from this videoWhat you will learn
- To find the probability of compound events.
- The difference between dependent and independent events.
- How this knowledge can help us pick outfits, win prizes and even play with puppies!
- Discussion Questions
Before Video
What is probability?ANSWERWe use probability to tell us how likely something is to occur. Probabilities have values from 0 to 1. A probability of 0 means something is impossible. A probability of 1 means something is certain.
Theoretical probability is a probability that is calculated. For events with equally-likely outcomes, the theoretical probability is the number of ways the event can happen divided by the total number of outcomes in the sample space.
ANSWERLikelihood increases with larger numbers. 0.5 is greater than 0.2, so it is more likely that your family has apple pie for dessert.
[ggfrac]1/2[/ggfrac] or 50%
[ggfrac]1/6[/ggfrac]
After Video
What are the methods you can use to find the probability of an independent compound event?ANSWERSample answers: make a table, draw a tree diagram, find the probabilities as single events and then multiply them to find the probability of the compound event
Once you have completed the first event, you need to see how the number of possible outcomes has changed for the second event. You also need to see if the number of favorable outcomes has changed.
ANSWERMake a table or list to show the outcomes:
H H H
H T H
H H T
H T T
T T T
T H T
T T H
T H H
Only one of these 8 outcomes is H H H, so the probability of getting 3 heads is 18.
or
The probability of getting heads on a toss of a coin is 12. So the probability of getting 3 heads when tossing 3 coins is [ggfrac] 1/2[/ggfrac] × [ggfrac] 1/2[/ggfrac] × [ggfrac] 1/2[/ggfrac], or [ggfrac] 1/8[/ggfrac].
Ms. Lee is having a dinner party. These are the choices for the menu:
Main dish: steak, chicken
Vegetable: corn, green beans, broccoli
Dessert: lemon tart, strawberry ice cream
She decides to choose something from each list randomly to create the menu. Create a tree diagram that shows the probability of having chicken, broccoli, and strawberry ice cream at her dinner party.
ANSWERThe tree diagram shows the choices of steak and chicken in the top row. Three branches from each main dishes show corn, green beans, and broccoli. Two branches from each vegetable show lemon tart and strawberry ice cream. The tree diagram shows that there are 12 different possibilities for the menu. Only one of those possibilities is chicken, broccoli, and strawberry ice cream. So the probability of having chicken, broccoli, and strawberry ice cream at her dinner party is [ggfrac]1/12[/ggfrac].
ANSWERThere are 6 blue marbles, 4 yellow marbles, and 10 total marbles for the first pick, so the probability of picking a blue marble is [ggfrac]6/10[/ggfrac], or [ggfrac]3/5[/ggfrac]. For the second pick, there are 5 blue marbles, 4 yellow marbles, and 9 total marbles, so the probability of picking a yellow marble for the second pick is [ggfrac]4/9[/ggfrac]. The probability of picking a blue marble on the first pick and a yellow marble on the second pick is [ggfrac]3/5[/ggfrac] × [ggfrac]4/9[/ggfrac] = [ggfrac]12/45[/ggfrac], or [ggfrac]4/15[/ggfrac].
- Vocabulary
- Probability DEFINE
The likelihood that an event occurs. Probability is expressed using numbers between 0 and 1.
- Event DEFINE
A set of possible outcomes that result from a particular experiment or situation.
- Compound Events DEFINE
Two or more events happening together.
- Dependent Events DEFINE
Events that depend on each other, where one event has an effect on another event.
- Independent Events DEFINE
Events that don’t depend on each other, where one event does not have an effect on other events.
- Impossible Event DEFINE
An event that has a probability of 0 of occurring.
- Certain Event DEFINE
An event that has a probability of 1 of occurring.
- Outcome DEFINE
Any potential result in an experiment. For example, when you flip a coin there are two outcomes: {heads, tails}.
- Tree Diagram DEFINE
A diagram that has branches and shows all the possible outcomes of an event.
- Probability DEFINE
- Reading Material
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- Practice Number Problems
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