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A deck of cards contains 52 cards, 26 red and 26 black. A card is chosen at random.

What is the probability that the card is black or a king?

$(P) = 26/52 + 4/52 = 30/52$

Is this correct?

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  • $\begingroup$ Calculate $P[black] + P[king] - P[black~and~king]$ (to avoid overcounting). $\endgroup$ – David G. Stork Oct 25 '17 at 22:19
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You forgot to subtract off the probability that a card is black and is a king i.e. $2/52$ (the king of clubs and spades). The correct probability is $$ 28/52. $$ We are using the fact that $$ P(A\cup B)=P(A)+P(B)-P(A\cap B) $$ where $A$ is the event of black card being drawn and $B$ is the event of a king card being drawn.

In your computation we are counting the king of spades and king of clubs twice which is why we subtract off the probability of the intersection.

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