Let $A , B$ , And $C$ Be Events in a Sample Space

question 11

Essay

Let $A , B$ , and $C$ be events in a sample space $S$ such that $S = A \cup B \cup C$ . Suppose that $P ( A ) = 0.3 , P ( B ) = 0.6$ , and $P ( A \cap B ) = 0.2$ . Find each of the following.
(a) $P ( A \cup B )$
(b) $P ( C )$
(c) $P \left( A ^ { c } \cup B ^ { c } \right)$

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Definitions:

Detention

The act of detaining someone or the state of being detained in a specific context, such as in schools as a form of punishment, or in immigration or law enforcement.

Sleep

A naturally recurring state of mind and body characterized by altered consciousness, relatively inhibited sensory activity, and inhibition of nearly all voluntary muscles.

Sigmund Freud

An Austrian neurologist known as the founding father of psychoanalysis, a method for treating psychological pathology by means of dialogue between the patient and a psychoanalyst.

Stages of Sleep

The progression through different phases of sleep characterized by unique brain wave activity, eye movements, and muscle tension, including REM and non-REM (NREM) stages.