MathematicsA card is drawn from a well-shuffled pack of 52 cards. Find the probability that it is a king of spades.

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that it is a king of spades.

  1. A
    1 52  
  2. B
    2 52  
  3. C
    3 52  
  4. D
    4 52   

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    Solution:

    Given that a card is drawn at random from a pack of 52 playing cards.
    We need to find the probability that the card drawn is a king of spades.
    Probability of an event E is defined as:
    P(E)=Number of favorable outcomesTotal number of possible outcomes
    A deck of cards contains 52 cards in it, that are 13 spade cards, 13 heart cards, 13 diamond cards and 13 club cards.
    Therefore, the total number of possible outcomes is 52.
    There is only one king of spade in the whole pack of cards.
    Therefore, the total number of favorable outcomes will be 1.
    Let E   be the event that the card drawn is king of spades.
    Now, the probability of getting a card which is king of spades is:
    P(E)= 1 52  
    Thus, the probability of getting a card which is king of spades is 1 52  .
    Therefore, option 1 is correct.
     
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