Here is the question : A card is drawn from a standard deck of 52 cards. Find the probability that the card is either a five or a black card. $[A] \frac4{ 13}[B] \frac{15}{26} [C] \frac{17}{52} [D] \frac{7}{13} $
I thought you have 2 cards that are both five and black, they should not be included in "either five or black " case, the probability is $\frac{4+26-2-2}{52}=\frac{1}{2}$. However, this is not one of the 4 choices. The only one that seems to be right is [D] $\frac{7}{13}$, in which case the two cards that are both 5 and black are included in the calculation. Should or shouldn't we include these two cards?