Last Updated Sep 27, 2025

Conditional Probability Simplified Revision Notes for Leaving Cert Mathematics

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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 $A$ given $B$ is:

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

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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.

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Step 2: Insert this data into the formula

$$P(\text{Ace} \mid \text{Red Card}) = \frac{P(\text{Ace and Red Card})}{P(\text{Red Card})}$$$$\frac{\frac{2}{52}}{\frac{26}{52}} = \frac{2}{26} = \frac{1}{13}$$

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