The events of choosing a number that is a multiple of [tex]3[/tex] or choosing a number that is a multiple of [tex]4[/tex] are not mutually exclusive.
Mutually Exclusive means when two sets have no common elements.
Not Mutually Exclusive means when two sets share common elements.
We have,
Cards numbered [tex]20[/tex] to [tex]30[/tex].
Let's
Set [tex]A =[/tex] Multiple of [tex]3[/tex]
i.e. Set [tex]A = \ \{ 21, 24,27,30\}[/tex]
Set [tex]B =[/tex] Multiple of [tex]4[/tex]
i.e. Set [tex]B = \{20,24,28\}[/tex]
So, Set [tex]A[/tex] and Set [tex]B[/tex] have common element [tex]24[/tex], so we call them Not Mutually Exclusive, from the mentioned definition we find out this.
Hence, we can say that the events of choosing a number that is a multiple of [tex]3[/tex] or choosing a number that is a multiple of [tex]4[/tex] are not mutually exclusive.
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