A card is drawn at random from a pack of cards. What is the probability that it is Either a King card or a Black Card.?

Question

Answer

Probability of drawing a King Card or a Black Card

When we draw a card from a pack of 52 cards, the probability of getting a specific card is 1/52. To calculate the probability of getting either a King card or a Black card, we need to consider the total number of King cards and Black cards in the pack.

Number of King Cards

A standard pack of cards has four King cards: King of Hearts, King of Diamonds, King of Clubs, and King of Spades.

Number of Black Cards

There are 26 black cards in a standard deck of cards: 13 Spades and 13 Clubs.

Calculating the Probability

To calculate the probability of drawing a King card or a Black card, we need to add the number of King cards and Black cards and then subtract the number of cards that are both King and Black (King of Spades and King of Clubs). This is because we only want to count these cards once.

So, the number of cards that are either King or Black is:

4 King cards + 26 Black cards - 2 King and Black cards = 28 cards

The total number of cards in the pack is 52. Therefore, the probability of drawing a King card or a Black card is:

28/52 = 7/13 or approximately 0.54

Conclusion

The probability of drawing either a King card or a Black card from a standard pack of 52 cards is 7/13 or approximately 0.54.

Answer

Probability of drawing either a King card or a Black Card

When we draw a card from a pack of cards, we have a total of 52 cards, which can be categorized into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. Out of these 13 cards, there are 4 King cards in the pack, and there are 26 black cards in the pack.

Probability of drawing a King card

The probability of drawing a King card from the pack can be calculated as follows:

Probability of drawing a King card = Number of King cards in the pack / Total number of cards in the pack

Probability of drawing a King card = 4/52 = 1/13

Probability of drawing a black card

The probability of drawing a black card from the pack can be calculated as follows:

Probability of drawing a black card = Number of black cards in the pack / Total number of cards in the pack

Probability of drawing a black card = 26/52 = 1/2

Probability of drawing either a King card or a Black card

When we want to calculate the probability of drawing either a King card or a Black card, we need to consider the following:

There are 4 King cards in the pack, out of which 2 are black (King of Spades and King of Clubs), and 2 are red (King of Hearts and King of Diamonds).

There are 26 black cards in the pack, out of which 2 are Jack cards (Jack of Spades and Jack of Clubs), and 2 are Queen cards (Queen of Spades and Queen of Clubs).

To calculate the probability of drawing either a King card or a Black card, we need to add the probability of drawing a King card to the probability of drawing a black card and then subtract the probability of drawing a King card that is not black:

Probability of drawing either a King card or a Black card = Probability of drawing a King card + Probability of drawing a black card - Probability of drawing a King card that is not black

Probability of drawing either a King card or a Black card = (2/52) + (26/52) - (2/52) = 26/52 = 1/2

Conclusion

The probability of drawing either a King card or a Black card from a pack of cards is 1/2 or 50%. This means that if we draw a card at random from the pack, there is an equal chance of drawing either a King card or a Black card.

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