Conditional Probability (Leaving Cert Mathematics): Revision Notes

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Conditional Probability

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. The conditional probability of AA given BB is:

P(A∣B)=P(A and B)P(B) P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}
infoNote

Example: In a deck of 52 cards, what is the probability of drawing an Ace given that a red card has been drawn?

Step 1: Work out the data in the probability question.

There are 26 red cards in the deck (13 Hearts and 13 Diamonds)

2 of these are Aces.

Step 2: Insert this data into the formula

P(Ace∣Red Card)=P(Ace and Red Card)P(Red Card)P(\text{Ace} \mid \text{Red Card}) = \frac{P(\text{Ace and Red Card})}{P(\text{Red Card})} 2522652=226=113\frac{\frac{2}{52}}{\frac{26}{52}} = \frac{2}{26} = \frac{1}{13}

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Explore Leaving Cert Mathematics Quizzes by Topics

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The Basics of Counting

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Explore Leaving Cert Mathematics Flashcards by Topics

Fundamentals of Probability

The Basics of Counting

Permutations / Arrangements

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Set Theory and Probability

Combined Events/Bernouilli Trials

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