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Mathematics · Ch 9 — Probability

Conditional Probability - Definition

9.3.1

Conditional Probability - Definition

So far every probability has been computed against the full sample space SS. Often, though, we already know something has happened, and we want the probability of a further event given that information. The conditional probability of event AA given that event BB has already occurred - written P(A/B)P(A/B), read 'A given B' - is defined whenever P(B)≠0P(B)\ne 0. …

Misc Ex1Face card given a red card is drawn

Worked out. Restricts the 52-card sample space to the 26 red cards, then counts how many of those are face cards. Working through this worked example after reading the theory above helps consolidate the method before attempting the exercise questions that follow it in the text …

Misc Ex2Sum divisible by 3 given the sum is odd

Worked out. Restricts the 36-outcome two-dice sample space to the 18 outcomes with an odd sum, then counts how many of those have a sum divisible by 3. Working through this worked example after reading the theory above helps consolidate the method before attempting the exercise questions that follow it in the te …