The total number of possible outcomes:
When two cards are drawn at random from a pack of 52 cards, the total number of possible outcomes is given by the combination formula. Since the order of drawing the cards doesn't matter, we use the combination formula instead of the permutation formula.
The total number of possible outcomes is given by:
nCr = (n!)/(r!(n-r)!)
Here, n = 52 (total number of cards in the deck) and r = 2 (number of cards drawn).
Total possible outcomes = 52C2 = (52!)/(2!(52-2)!) = (52!)/(2!50!) = (52*51)/2 = 1326

Probability that both cards are black:
There are 26 black cards in a deck of 52 cards (clubs and spades), so the probability of drawing the first black card is 26/52. After the first black card is drawn, there are 25 black cards left out of the remaining 51 cards. So, the probability of drawing the second black card is 25/51.
To find the probability that both cards are black, we multiply the probabilities of each event:
P(both black) = (26/52) * (25/51) = 325/1326

Probability that both cards are queens:
There are 4 queens in a deck of 52 cards, so the probability of drawing the first queen is 4/52. After the first queen is drawn, there are 3 queens left out of the remaining 51 cards. So, the probability of drawing the second queen is 3/51.
To find the probability that both cards are queens, we multiply the probabilities of each event:
P(both queens) = (4/52) * (3/51) = 12/1326

Probability that either both are black or both are queens:
To find the probability that either both cards are black or both cards are queens, we need to consider two cases:
1. Both cards are black and not queens: We already calculated this probability as 325/1326.
2. Both cards are queens and not black: We calculated this probability as 12/1326.

To find the probability of either of these cases occurring, we add the probabilities together:
P(either both black or both queens) = P(both black and not queens) + P(both queens and not black)
P(either both black or both queens) = 325/1326 + 12/1326 = 337/1326

Final Answer:
The probability that either both cards are black or both cards are queens is 337/1326.