if one card is selected at random from a standard deck of 52 cards, what is the probability of choosing a black card or a king?
Black card = 26/52 = 1/2
King = 4/52 = 1/13
To find either-or probability, add the individual probabilities.
To find the probability of choosing a black card or a king from a standard deck of 52 cards, we need to first determine the number of favorable outcomes and the total number of possible outcomes.
1. Determine the number of black cards:
In a standard deck, there are 26 black cards (13 clubs ♣️ and 13 spades ♠️).
2. Determine the number of kings:
In a standard deck, there are 4 kings (king of clubs ♣️, king of spades ♠️, king of hearts ♥️, and king of diamonds ♦️).
3. Find the number of cards that are both black and kings (overlapping):
There are 2 cards that are both black and kings (king of clubs ♣️ and king of spades ♠️).
4. Calculate the total number of favorable outcomes:
The number of black cards (26) + the number of kings (4) - the overlapping cards (2) = 26 + 4 - 2 = 28.
5. Determine the total number of possible outcomes:
In a standard deck, there are 52 cards.
6. Calculate the probability:
Probability = Favorable outcomes / Total outcomes
Probability = 28/52
Simplifying, probability = 7/13.
Therefore, the probability of choosing a black card or a king from a standard deck of 52 cards is 7/13.
To find the probability of choosing a black card or a king from a standard deck of 52 cards, we need to first determine the number of favorable outcomes and the total number of possible outcomes.
First, let's count the number of black cards in a standard deck. A standard deck contains 26 black cards (clubs and spades), as there are 13 of each.
Next, let's count the number of kings in the deck. There are 4 kings in total (king of hearts, king of diamonds, king of clubs, and king of spades).
Now, we need to determine if there are any cards that are both black cards and kings. In this case, there are 2 cards that satisfy both conditions: the king of clubs and the king of spades. Since we don't want to count these twice, we subtract them from our total count.
So, the number of favorable outcomes (black cards or kings) is 26 + 4 - 2 = 28.
The total number of possible outcomes is 52, as there are 52 cards in a standard deck.
Therefore, the probability of choosing a black card or a king is 28/52, which simplifies to 7/13.