Three coins are tossed. Describe three events which are mutually exclusive but not 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 but not exhaustive can be defined as:
$A$: Getting exactly three heads,i.e.,$A = \{HHH\}$
$B$: Getting exactly one head,i.e.,$B = \{HTT, THT, TTH\}$
$C$: Getting exactly two heads,i.e.,$C = \{HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = \phi$,$B \cap C = \phi$,and $C \cap A = \phi$.
They are not exhaustive because $A \cup B \cup C = \{HHH, HTT, THT, TTH, HHT, HTH, THH\} \neq S$ (since $TTT \notin A \cup B \cup C$).
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Three events that are mutually exclusive but not exhaustive can be defined as:
$A$: Getting exactly three heads,i.e.,$A = \{HHH\}$
$B$: Getting exactly one head,i.e.,$B = \{HTT, THT, TTH\}$
$C$: Getting exactly two heads,i.e.,$C = \{HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = \phi$,$B \cap C = \phi$,and $C \cap A = \phi$.
They are not exhaustive because $A \cup B \cup C = \{HHH, HTT, THT, TTH, HHT, HTH, THH\} \neq S$ (since $TTT \notin A \cup B \cup C$).
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