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Mathematics

A card is drawn at random from a pack of 52 playing cards. The probability of drawing a card which is neither a spade nor a king, is:

  1. (1752)\Big(\dfrac{17}{52}\Big)

  2. (413)\Big(\dfrac{4}{13}\Big)

  3. (3552)\Big(\dfrac{35}{52}\Big)

  4. (913)\Big(\dfrac{9}{13}\Big)

Probability

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Answer

A standard deck of playing cards contains 52 cards.

Total number of outcomes = 52

There are 13 spade cards and each suit has 1 king.

So, the other 3 suits apart from spade has kings.

∴ Total no. of spade and king cards = 13 + 3 = 16.

Hence, no. of cards other than spade and king = 52 - 16 = 36.

Let E be the event of choosing neither a spade nor a king, then

The number of favorable outcomes to the event E = 36

∴ P(E) = Number of favorable outcomesTotal number of outcomes=3652=913\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{36}{52} = \dfrac{9}{13}

Hence, option 4 is the correct option.

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