Probability and Distributions Checkpoint
A free Statistics and Data Analysis lesson from the “Probability and Distributions” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews probability models, conditional probability, independence, tree diagrams, expected value, binomial reasoning, and normal models.
What you'll learn
- Review the major skills from this part of the course
- Choose an appropriate statistical method
- Explain results in context
Worked example
Problem. If P(A) = 0.35, what is P(not A)?
- Complements add to 1.
- Subtract P(A) from 1.
Answer: 0.65
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Review case A: If P(A) = 0.35, what is P(not A)?
Show solution
- Complements add to 1.
- Subtract P(A) from 1.
Answer: 0.65
2. Review case B: Events A and B are disjoint. If P(A) = 0.2 and P(B) = 0.5, what is P(A or B)?
Show solution
- For disjoint events, add the probabilities.
- There is no overlap to subtract.
Answer: 0.7
3. Review case C: Among 8 students in a group, 3 play soccer. What is P(plays soccer | in this group)?
Show solution
- The condition sets the denominator to this group.
- 3/8 simplifies to 3/8.
Answer: 3/8
4. Review case D: If two events are independent, then P(B | A) equals:
Choices: P(A) - P(B) · P(B) · P(A) + P(B) · 0
Show solution
- Independence means knowing A happened does not change B.
- So P(B | A) = P(B).
Answer: P(B)
5. Review case E: A fair coin is flipped 3 times. What is the probability of HHH?
Show solution
- Each heads has probability 1/2.
- (1/2)^3 = 1/8.
Answer: 1/8
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