Answer:
[tex]\dfrac{25}{26}[/tex]
Step-by-step explanation:
Let
- D be the event that the card drawn is a black card
- F be the event that the card drawn is a 10 card
- F' be the event that the card drawn is not a 10 card
The probability
[tex]Pr(D\cup F')=Pr(D)+Pr(F')-Pr(D\cap F')\\[/tex]
Note that
[tex]Pr(D)=\dfrac{26}{52}=\dfrac{1}{2}\\ \\Pr(F)=\dfrac{4}{52}=\dfrac{1}{13}\\ \\Pr(F')=1-\dfrac{1}{13}=\dfrac{12}{13}\\ \\Pr(D\cap F')=\dfrac{24}{52}=\dfrac{6}{13}[/tex]
So,
[tex]Pr(D\cup F')=\dfrac{1}{2}+\dfrac{12}{13}-\dfrac{6}{13}=\dfrac{25}{26}[/tex]
