Mutually Exclusive Events – The Addition Rule (Leaving Cert Mathematics): Quizzes

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Mutually Exclusive Events – The Addition Rule
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What does it mean for two events to be mutually exclusive?

They cannot occur simultaneously

What is the addition rule for mutually exclusive events AA and BB?

P(A or B)=P(A)+P(B)P(A \text{ or } B) = P(A) + P(B)

What is another name for the addition rule?

The OR rule

If P(A)=37P(A) = \frac{3}{7} and P(B)=27P(B) = \frac{2}{7} (mutually exclusive), find P(A or B)P(A \text{ or } B).

57\frac{5}{7}

Why must we subtract P(A and B)P(A \text{ and } B) in the general addition rule?

To avoid counting overlaps twice

What is the general addition rule when events can overlap?

P(A or B)=P(A)+P(B)−P(A and B)P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)

On a dice, are 'score is 3' and 'score is even' mutually exclusive?

Yes, 3 is odd so cannot be even

On a dice, are 'score is even' and 'score > 4' mutually exclusive?

No, 6 is both even and > 4

On a dice, are 'score is prime' and 'score is even' mutually exclusive?

No, 2 is both prime and even

What question should you ask to test if events are mutually exclusive?

Can these events happen simultaneously?

If P(A)=1030P(A) = \frac{10}{30}, P(B)=630P(B) = \frac{6}{30}, P(A and B)=230P(A \text{ and } B) = \frac{2}{30}, find P(A or B)P(A \text{ or } B).

1430\frac{14}{30}

What is the most common mistake when calculating 'or' probabilities with overlapping events?

Double counting the intersection

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