We have to find the probability that you are dealt a ten or a black card.
Out of the 52 card deck, there are 26 black cards.
There are also 4 cards that are tens, but there are 2 cards that are both black and tens.
Then, if we define B: the event of a black card and T: the event of a ten, we can calculate the probability of B or T as:
[tex]P(B\cup T)=P(B)+P(T)-P(B\cap T)[/tex]Replacing with the values of the probability (success events divided by the total possible events), we can solve this as:
[tex]\begin{gathered} P(B\cup T)=P(B)+P(T)-P(B\cap T) \\ P(B\cup T)=\frac{21}{52}+\frac{4}{52}-\frac{2}{52} \\ P(B\cup T)=\frac{21+4-2}{52} \\ P(B\cup T)=\frac{23}{52} \end{gathered}[/tex]Answer: the probability of getting a black or a ten is 23/52.
