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Mathematics

One card is drawn at random from a pack of 52 playing cards. The probability that the card drawn is either a red card or a king is:

  1. (12)\Big(\dfrac{1}{2}\Big)

  2. (613)\Big(\dfrac{6}{13}\Big)

  3. (713)\Big(\dfrac{7}{13}\Big)

  4. (2752)\Big(\dfrac{27}{52}\Big)

Probability

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Answer

A standard deck of playing cards contains 52 cards.

Total number of outcomes = 52

There are 26 red cards (13 hearts and 13 diamonds) and 4 kings in a deck, 2 of these kings (King of Hearts and King of Diamonds) are red.

Hence, no. of cards which are red or king = 26 Red Cards + 2 Black Kings = 28

Let E be the event of choosing either a red card or a king , then

The number of favorable outcomes to the event E = 28

∴ P(E) = Number of favorable outcomesTotal number of outcomes=2852=713\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{28}{52} = \dfrac{7}{13}

Hence, option 3 is the correct option.

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