Introduction to Probability - AP Statistics

1. Identify the correct representation for the intersection of events $A$ and $B$.

   $A \text{ and } B$. Intersection notation for events occurring together.

2. Identify the probability of a certain event.

   The probability of a certain event is 1. An event that must occur has probability 1.

3. Identify the probability of rolling a number greater than 4 on a six-sided die.

   $\frac{1}{3}$. Numbers 5 and 6 out of six possibilities.

4. What is the probability of an event that is certain to happen?

   The probability is 1. Certain events have maximum probability.

5. What is the probability of drawing a red card from a standard deck?

   $\frac{1}{2}$. 26 red cards (hearts and diamonds) out of 52.

6. State the probability of rolling a 3 on a fair six-sided die.

   $\frac{1}{6}$. One favorable outcome out of six possible.

7. What is meant by the sample space in probability?

   The sample space is the set of all possible outcomes. Contains every possible outcome of an experiment.

8. What is the multiplication rule for dependent events?

   $P(A \text{ and } B) = P(A) \times P(B|A)$. Multiplies probability of first by conditional probability.

9. Choose the correct expression for the complement rule.

   $P(E') = 1 - P(E)$. Standard complement rule formula.

10. What does it mean if two events are independent?

    The occurrence of one event does not affect the probability of the other. Knowledge of one event doesn't change the other's probability.

11. Define what a 'simple event' is in probability.

    A simple event consists of a single outcome. Contains exactly one outcome from the sample space.

12. State the formula for conditional probability.

    $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$. Divides joint probability by the given event's probability.

13. Identify the probability of a single coin landing heads up.

    $\frac{1}{2}$. Two equally likely outcomes: heads or tails.

14. What is the probability of independent events $A$ and $B$ both occurring?

    $P(A \text{ and } B) = P(A) \times P(B)$. For independent events, multiply individual probabilities.

15. What is the probability of either event $A$ or event $B$ if they are mutually exclusive?

    $P(A \text{ or } B) = P(A) + P(B)$. Mutually exclusive means no overlap, so probabilities add.

16. What is the probability of drawing a heart from a standard deck of cards?

    $\frac{1}{4}$ or 0.25. 13 hearts out of 52 total cards.

17. Identify the term for $P(A|B)$.

    Conditional probability. Represents probability of A given that B occurred.

18. State the formula for the probability of $A$ or $B$ when $A$ and $B$ are not mutually exclusive.

    $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. General addition rule accounting for overlap.

19. Define conditional probability.

    Conditional probability is the probability of an event given another event. Probability of one event assuming another has occurred.

20. Define the term 'event' in probability.

    An event is a set of outcomes from a probability experiment. A collection of one or more outcomes.

21. Find the probability of rolling an even number on a six-sided die.

    $\frac{1}{2}$. Three even numbers (2, 4, 6) out of six total.

22. Define what a probability distribution is.

    A probability distribution lists all the possible outcomes and their probabilities. Maps each outcome to its probability value.

23. What is the probability of the complement of an event?

    $P(E') = 1 - P(E)$. Complement probability equals 1 minus the event probability.

24. Calculate $P(A \text{ and } B)$ given $P(A) = 0.4$, $P(B) = 0.5$, and $A$ and $B$ are independent.

    $P(A \text{ and } B) = 0.2$. Multiply probabilities: $0.4 \times 0.5 = 0.2$.

25. What is the probability of drawing an ace from a standard deck of cards?

    $\frac{1}{13}$. Four aces in a standard 52-card deck.

26. Calculate $P(A')$ if $P(A) = 0.7$.

    $P(A') = 0.3$. Using complement rule: $1 - 0.7 = 0.3$.

27. Define mutually exclusive events.

    Mutually exclusive events cannot occur at the same time. Events with no shared outcomes.

28. Determine if events $A$ and $B$ are independent given $P(A|B) = P(A)$.

    Events $A$ and $B$ are independent. When conditional equals marginal probability, events are independent.

29. If $P(A) = 0.3$ and $P(B) = 0.6$, find $P(A \text{ or } B)$ if $A$ and $B$ are mutually exclusive.

    $P(A \text{ or } B) = 0.9$. Add probabilities since events cannot overlap.

30. Choose the correct term for $P(E')$.

    Complement of event $E$. Standard notation for the complement of event E.

31. What is the range of values for probability?

    Probability values range from 0 to 1. 0 means impossible, 1 means certain.

32. State the addition rule for mutually exclusive events.

    $P(A \text{ or } B) = P(A) + P(B)$. For mutually exclusive events, probabilities simply add.

33. State the formula for the probability of an event.

    $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

34. Identify the probability of an impossible event.

    The probability of an impossible event is 0. An event that cannot occur has zero probability.

35. Choose the term for $P(A \text{ and } B)$ when $A$ and $B$ are independent.

    Joint probability. Describes the probability of both events occurring together.

36. What is the definition of probability?

    Probability is the measure of the likelihood of an event occurring. Quantifies the likelihood on a scale from 0 to 1.

37. State the general addition rule for any two events.

    $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. Subtracts overlap to avoid double-counting.

38. What does $P(\text{not } A)$ represent?

    The probability that event $A$ does not occur. Standard notation for complement probability.

39. What does the term 'outcome' refer to in probability?

    An outcome is a possible result of a probability experiment. A single possible result from an experiment.

Study these flashcards