AP Stats Probability and Distributions 1 — Questions and Answers
Question 1: What is the probability of an impossible event?
- 0 (Correct answer)
- 1
- 0.5
- Undefined
Correct answer: 0
An impossible event has a probability of 0, meaning it can never occur.
Question 2: What is the difference between independent and dependent events?
- Independent events do not affect each others probability; dependent events do (Correct answer)
- They are the same thing
- Independent events always occur together
- Dependent events cannot occur simultaneously
Correct answer: Independent events do not affect each others probability; dependent events do
Independent events have no influence on each other, while the occurrence of a dependent event changes the probability of the other.
Question 3: What does the Law of Large Numbers state?
- As sample size increases, the sample mean approaches the population mean (Correct answer)
- Large samples are always better than small samples
- Probability is only valid for large numbers
- Large numbers always produce normal distributions
Correct answer: As sample size increases, the sample mean approaches the population mean
The Law of Large Numbers states that as the number of trials increases, the experimental probability converges to the theoretical probability.
Question 4: What is conditional probability?
- The probability of an event given that another event has already occurred (Correct answer)
- The probability that is conditional on sample size
- A probability that changes over time
- The probability of two events occurring simultaneously
Correct answer: The probability of an event given that another event has already occurred
Conditional probability P(A|B) measures the likelihood of event A occurring given that event B has already happened.
Question 5: What is Bayes Theorem used for?
- Updating probabilities based on new evidence (Correct answer)
- Calculating the mean of a population
- Determining sample size requirements
- Measuring correlation between variables
Correct answer: Updating probabilities based on new evidence
Bayes Theorem provides a mathematical framework for updating prior probabilities with new evidence to calculate posterior probabilities.
Question 6: What is a normal distribution?
- A symmetric, bell-shaped distribution where most values cluster around the mean (Correct answer)
- Any distribution with a known mean
- A distribution with exactly two modes
- A distribution that only applies to sample data
Correct answer: A symmetric, bell-shaped distribution where most values cluster around the mean
The normal distribution is bell-shaped with symmetry around the mean, with about 68% of data within one standard deviation.
AP Stats Probability and Distributions 1
What is the probability of an impossible event?