Combined Events/Bernouilli Trials (Leaving Cert Mathematics): Flashcards

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Combined Events
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Formula for P(A or B)P(A \text{ or } B)

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

Meaning of 'A or B' in probability

Either event A or event B (or both) occur

Formula for P(A and B)P(A \text{ and } B) (dependent events)

P(A)×P(B∣A)P(A) \times P(B \mid A)

P(Heart)P(\text{Heart}) from standard deck

1352=14\frac{13}{52} = \frac{1}{4}

P(Ace)P(\text{Ace}) from standard deck

452=113\frac{4}{52} = \frac{1}{13}

P(Heart or Ace)P(\text{Heart or Ace}) from deck

1652=413\frac{16}{52} = \frac{4}{13}

P(First Ace)P(\text{First Ace}) from deck

452=113\frac{4}{52} = \frac{1}{13}

P(Second Ace)P(\text{Second Ace}) without replacement

351=117\frac{3}{51} = \frac{1}{17}

P(Two Aces)P(\text{Two Aces}) without replacement

113×117=1221\frac{1}{13} \times \frac{1}{17} = \frac{1}{221}

Why subtract P(A and B)P(A \text{ and } B) in union formula?

To avoid counting the overlap twice

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