Question

you are dealt one card from a 52 - card deck. find the probability that you are dealt an eight or a black card. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a fraction. simplify your answer)

Explanation:

Step1: Calculate the number of eights

There are 4 eights in a deck ($n(Eight)=4$).

Step2: Calculate the number of black cards

There are 26 black cards in a deck ($n(Black) = 26$).

Step3: Calculate the number of black eights

There are 2 black eights (8 of spades and 8 of clubs), so $n(Eight\cap Black)=2$.

Step4: Use the formula for the probability of the union of two events

The formula is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of getting an eight and $B$ is the event of getting a black card.
The total number of cards $n(Total) = 52$.
$P(Eight)=\frac{n(Eight)}{n(Total)}=\frac{4}{52}$, $P(Black)=\frac{n(Black)}{n(Total)}=\frac{26}{52}$, and $P(Eight\cap Black)=\frac{n(Eight\cap Black)}{n(Total)}=\frac{2}{52}$.
Then $P(Eight\cup Black)=\frac{4 + 26- 2}{52}=\frac{28}{52}=\frac{7}{13}$.

Answer:

$\frac{7}{13}$