Three coins are tossed. Describe two events which are mutually exclusive but not exhaustive.
(N/A) When three coins are tossed,the sample space $S$ is given by:
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events which are mutually exclusive but not exhaustive can be defined as:
$A$: Getting exactly one head.
$B$: Getting exactly one tail.
Here,the sets are:
$A = \{HTT, THT, TTH\}$
$B = \{HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = \phi$.
They are not exhaustive because $A \cup B = \{HTT, THT, TTH, HHT, HTH, THH\} \neq S$.
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events which are mutually exclusive but not exhaustive can be defined as:
$A$: Getting exactly one head.
$B$: Getting exactly one tail.
Here,the sets are:
$A = \{HTT, THT, TTH\}$
$B = \{HHT, HTH, THH\}$
These events are mutually exclusive because $A \cap B = \phi$.
They are not exhaustive because $A \cup B = \{HTT, THT, TTH, HHT, HTH, THH\} \neq S$.
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