Algebra of events — lesson. Mathematics State Board, Class 10.

UPSKILL MATH PLUS

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Let

$A$ and

$B$ are the events of a random experiment.

Let

$S$ be the sample space where

$A \subseteq S$ and

$B \subseteq S$ .

Based on the occurrence of the events

$A$ and

$B$ , we shall discuss certain algebraic property.

The events

$(A \cup B)$ occurs only when at least one of the events

$A$ or

$B$ occurs.

This event is depicted using the Venn diagram as follows:

The events

$(A \cap B)$ occurs only when both the events

$A$ and

$B$ occurs.

This event is depicted using the Venn diagram as follows:

The event

$\overline A$ occurs only when the event

$A$ does not occurs.

This event is depicted using the Venn diagram as follows:

The event

$\overline B$ occurs only when the event

$B$ does not occurs.

This event is depicted using the Venn diagram as follows:

Important!

$P(A \cup \overline A) = S$
$P(A \cap \overline A) = \phi$
$\overline {A \cup B} = \overline A \cap \overline B$ represents the event when neither $A$ nor $B$ happens.
If the events $A$ and $B$ are mutually exclusive, then $P(A \cup B) = P(A) + P(B)$ .
$P(\text{Union of events}) = \sum(\text{ Probability of events})$

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1. Algebra of events