Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are D and C mutually exclusive?
Accepted Solution
A:
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.