Question

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?

Answer 1

Answer:

Events D and C are mutually exclusive.

Step-by-step explanation:

Two events D and C are mutually exclusive if

$Pr(D\cup C)=Pr(D)+Pr(C)$

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

$Pr(D)=\dfrac{13}{52}=\dfrac{1}{4}$

The probabilty of chosing club is

$Pr(C)=\dfrac{13}{52}=\dfrac{1}{4}$

The probabilty of chosing diamond or club is

$Pr(D\cup C)=\dfrac{13+13}{52}=\dfrac{1}{2}$

Since

$\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{1}{4},$

events D and C are mutually exclusive.