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Mathematics

One card is drawn at random from a pack of 52 playing cards. What is the probability that the card drawn is a face card?

  1. (113)\Big(\dfrac{1}{13}\Big)

  2. (313)\Big(\dfrac{3}{13}\Big)

  3. (14)\Big(\dfrac{1}{4}\Big)

  4. (952)\Big(\dfrac{9}{52}\Big)

Probability

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Answer

A standard deck of playing cards contains 52 cards.

Total number of outcomes = 52

Let E be the event of choosing a face card , then

There are 4 suits in a deck, and each suit has 3 face cards.

The number of favorable outcomes to the event E = 4 suits × 3 face cards = 12

∴ P(E) = Number of favorable outcomesTotal number of outcomes=1252=313\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{12}{52} = \dfrac{3}{13}

Hence, option 2 is the correct option.

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