Three coins are tossed. Describe two events,which are not mutually exclusive.
(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 that are not mutually exclusive can be defined as:
$A$: Getting three heads
$B$: Getting at least $2$ heads
Here,the sets are:
$A = \{HHH\}$
$B = \{HHH, HHT, HTH, THH\}$
Since $A \cap B = \{HHH\} \neq \phi$,the events $A$ and $B$ are not mutually exclusive.
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events that are not mutually exclusive can be defined as:
$A$: Getting three heads
$B$: Getting at least $2$ heads
Here,the sets are:
$A = \{HHH\}$
$B = \{HHH, HHT, HTH, THH\}$
Since $A \cap B = \{HHH\} \neq \phi$,the events $A$ and $B$ are not mutually exclusive.
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