Mutually Exclusive Events - AP Statistics

1. Can mutually exclusive events be independent? Yes or No.

   No. If one occurs, the other has zero probability.

2. Find $P(A \text{ and } B)$ for mutually exclusive events $A$ and $B$.

   $P(A \text{ and } B) = 0$. Mutually exclusive events have no intersection.

3. State the probability of intersection for mutually exclusive events.

   $P(A \text{ and } B) = 0$. No common outcomes exist between the events.

4. What is another term for mutually exclusive events?

   Disjoint events. Alternative terminology for the same concept.

5. If $P(A \text{ or } B) = 1$, and $A$ and $B$ are mutually exclusive, what must be true?

   $P(A) + P(B) = 1$. They form complementary exhaustive events.

6. What does it mean for two events to be mutually exclusive?

   Two events cannot occur simultaneously. Events have no overlap in their outcomes.

7. For mutually exclusive events $A$ and $B$, $P(A) = 0.4$. Find $P(B)$ if $P(A \text{ or } B) = 0.7$.

   $P(B) = 0.3$. Use $P(A \text{ or } B) = P(A) + P(B)$ and solve.

8. Are drawing a face card or a non-face card mutually exclusive?

   Yes, they are mutually exclusive. Face and non-face cards are complementary categories.

9. If events are mutually exclusive, what is their joint probability?

   Zero. Events have no intersection by definition.

10. If events $A$ and $B$ are mutually exclusive, find $P(A \text{ and } B)$.

    $P(A \text{ and } B) = 0$. No overlap between mutually exclusive events.

11. What is the probability of the union of two mutually exclusive events?

    The sum of their individual probabilities. Since they cannot occur together, probabilities add directly.

12. Can mutually exclusive events have non-zero intersection probability?

    No, the intersection probability is zero. By definition, intersection probability must be zero.

13. What must be true about $P(A \text{ and } B)$ for mutually exclusive events?

    It must be zero. Defining requirement for mutual exclusivity.

14. If $P(A) = 0.3$ and $P(B) = 0.5$, and $A$ and $B$ are mutually exclusive, find $P(A \text{ or } B)$.

    $P(A \text{ or } B) = 0.8$. Add probabilities: $0.3 + 0.5 = 0.8$.

15. What happens to the probability of mutually exclusive events occurring together?

    Probability is zero. By definition, they cannot occur together.

16. State the formula for the probability of mutually exclusive events.

    $P(A \text{ or } B) = P(A) + P(B)$. No intersection term since $P(A \text{ and } B) = 0$.

17. If $A$ and $B$ are mutually exclusive, does $P(A \text{ and } B) > 0$? Yes or No.

    No. Intersection probability is always zero.

18. Are selecting a king or an ace from a deck mutually exclusive?

    Yes, they are mutually exclusive. One card cannot have multiple ranks.

19. For mutually exclusive events, is $P(A \text{ and } B)$ ever greater than zero?

    No, it is not greater than zero. Intersection probability is always zero by definition.

20. If $P(A)=0.4$ and $P(B)=0.5$ and they are mutually exclusive, find $P(A \text{ or } B)$.

    $P(A \text{ or } B) = 0.9$. Add probabilities: $0.4 + 0.5 = 0.9$.

21. For mutually exclusive events, what does $P(A \text{ or } B)$ equal?

    $P(A) + P(B)$. No intersection allows direct addition of probabilities.

22. Identify whether these events are mutually exclusive: rolling a 3 or 4 on a die.

    Yes, they are mutually exclusive. Each outcome is distinct with no overlap.

23. If $A$ and $B$ are mutually exclusive, what is $P(A \text{ and } B)$?

    $P(A \text{ and } B) = 0$. Fundamental property of mutually exclusive events.

24. Are choosing a vowel or consonant from the alphabet mutually exclusive?

    Yes, they are mutually exclusive. Letters are either vowels or consonants, not both.

25. If events $A$ and $B$ are mutually exclusive, what is $P(A \text{ or } B)$?

    $P(A) + P(B)$. No intersection term needed for mutually exclusive events.

26. Determine if these events are mutually exclusive: drawing a heart or a club from a deck.

    Yes, they are mutually exclusive. Different suits cannot overlap on one card.

27. What is the joint probability of mutually exclusive events?

    Zero. Events cannot occur simultaneously.

28. If events $A$ and $B$ are mutually exclusive, what is $P(A \text{ and } B)$?

    $P(A \text{ and } B) = 0$. Defining characteristic of mutual exclusivity.

29. Are rolling an even number and an odd number on a die mutually exclusive?

    Yes, they are mutually exclusive. No number can be both even and odd.

30. If $A$ and $B$ are mutually exclusive with $P(A)=0.2$ and $P(B)=0.6$, find $P(A \text{ or } B)$.

    $P(A \text{ or } B) = 0.8$. Add probabilities: $0.2 + 0.6 = 0.8$.

31. Identify if the events are mutually exclusive: flipping heads and tails on one coin toss.

    Yes, they are mutually exclusive. One coin flip produces exactly one outcome.

32. Find $P(A \text{ or } B)$ if $P(A)=0.3$, $P(B)=0.2$, and $A$ and $B$ are mutually exclusive.

    $P(A \text{ or } B) = 0.5$. Add probabilities: $0.3 + 0.2 = 0.5$.

33. If $A$ and $B$ are mutually exclusive with $P(A)=0.6$, find $P(B)$ if $P(A \text{ or } B)=0.9$.

    $P(B) = 0.3$. Solve $0.9 = 0.6 + P(B)$ to get $P(B) = 0.3$.

34. Identify if selecting a red or blue ball from a bag is mutually exclusive.

    Yes, it is mutually exclusive. One ball cannot have multiple colors.

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