Conditional and Independent Events
Ages 16–18Difficulty adapts to you
Conditional and Independent Events
Conditional probability restricts the sample space after information is known. Independent events do not change each other's probability, so P(A and B) = P(A)P(B) for independent events. Without independence, use a tree or conditional probabilities.
Your goals
- ✓You can understand how information changes probability and when events do or do not affect one another.
- ✓You can use Conditional and Independent Events, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Conditional and Independent Events:
- Understand how information changes probability and when events do or do not affect one another.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1From a bag with 3 red and 2 blue counters, after a red counter is not replaced, the next probability changes to 2 red out of 4.
- 2Two fair coin tosses are independent, so P(two heads) = 1/2 × 1/2 = 1/4.
Check these
- • Do not skip the meaning of a term or give a result without explaining what it means.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own conditional and independent events example, solve it, and explain how you checked it.
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Helpful Hints“If you are stuck, skip and come back later.”