Answer:
[tex]P(A\cup B)=\frac{4}{13}[/tex]
Step-by-step explanation:
Given:
Total number of cards = 52
Number of jacks = 4
Number of club cards = 13
Number of jacks and club cards = 1
Let event A represents the jack and event B represents the club card.
[tex]P(A)=\frac{4}{52}[/tex]
[tex]P(B)=\frac{13}{52}[/tex]
[tex]P(A\cap B)=\frac{1}{52}[/tex]
The formula for probability of union is
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]P(A\cup B)=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}[/tex]
[tex]P(A\cup B)=\frac{4+13-1}{52}[/tex]
[tex]P(A\cup B)=\frac{16}{52}[/tex]
[tex]P(A\cup B)=\frac{4}{13}[/tex]
Therefore, the probability of a jack or club card is [tex]\frac{4}{13}[/tex].
