Three coins are tossed. Describe three events which are mutually exclusive and exhaustive.
(N/A) When three coins are tossed,the sample space $S$ is given by:
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Three events that are mutually exclusive and exhaustive can be defined as:
$A$: Getting no heads.
$B$: Getting exactly one head.
$C$: Getting at least two heads.
These events are represented as:
$A = \{TTT\}$
$B = \{HTT, THT, TTH\}$
$C = \{HHH, HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = B \cap C = C \cap A = \phi$.
They are exhaustive because $A \cup B \cup C = S$.
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Three events that are mutually exclusive and exhaustive can be defined as:
$A$: Getting no heads.
$B$: Getting exactly one head.
$C$: Getting at least two heads.
These events are represented as:
$A = \{TTT\}$
$B = \{HTT, THT, TTH\}$
$C = \{HHH, HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = B \cap C = C \cap A = \phi$.
They are exhaustive because $A \cup B \cup C = S$.
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