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From a well shuffled deck of Playing cards, black jacks, black queens and black kings are removed. Now a card is drawn from the pack. Find the probability of not getting a diamond card.

Question

From a well shuffled deck of Playing cards, black jacks, black queens and black kings are removed. Now a card is drawn from the pack. Find the probability of not getting a diamond card.

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Solution

Sure, let's solve this step by step:

  1. A standard deck of playing cards has 52 cards. It consists of 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: A through 10, and three picture cards: Jack, Queen, and King. So, there are 13 diamond cards in a deck.

  2. According to the problem, black jacks, black queens, and black kings are removed. These are the Jack, Queen, and King of clubs and spades. So, 6 cards are removed.

  3. After removing these 6 cards, the total number of cards left in the deck is 52 - 6 = 46 cards.

  4. The number of diamond cards remains the same, which is 13.

  5. The probability of drawing a diamond card is the number of diamond cards divided by the total number of cards, which is 13/46.

  6. However, the problem asks for the probability of not getting a diamond card. The probability of an event not happening is 1 minus the probability of the event happening.

  7. So, the probability of not getting a diamond card is 1 - (13/46) = 33/46.

So, the probability of not getting a diamond card from the deck, after removing the black jacks, black queens, and black kings, is 33/46.

This problem has been solved

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