Answer:
Events D and C are mutually exclusive.
Step-by-step explanation:
Two events D and C are mutually exclusive if
[tex]Pr(D\cup C)=Pr(D)+Pr(C)[/tex]
Find these probabilities. In a standard deck of 52 playing cards there are 13 diamond cards and 13 club cards.
The probabilty of chosing diamond is
[tex]Pr(D)=\dfrac{13}{52}=\dfrac{1}{4}[/tex]
The probabilty of chosing club is
[tex]Pr(C)=\dfrac{13}{52}=\dfrac{1}{4}[/tex]
The probabilty of chosing diamond or club is
[tex]Pr(D\cup C)=\dfrac{13+13}{52}=\dfrac{1}{2}[/tex]
Since
[tex]\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{1}{4},[/tex]
events D and C are mutually exclusive.
