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What is the probability of drawing a face card from a standard deck?

This is a basic probability question because you can count favourable outcomes directly and divide by the total equally likely single-card outcomes.

Probability result

23.0769%

Exact fraction: 3/13

Decimal: 0.230769

The probability is 3/13, which is 0.230769 or 23.0769%.

A standard deck has 12 face cards because each suit has a jack, queen, and king. That makes the probability 12 out of 52, which reduces to 3 out of 13.

Worked steps

Show your work

  1. Inputs: favorable outcomes = 12, total outcomes = 52.
  2. Formula: P(E) = favorable outcomes / total outcomes.
  3. Substitute: P(E) = 12/52.
  4. Reduce: 12/52 = 3/13.
  5. Result: The probability is 3/13, which is 0.230769 or 23.0769%.

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A standard deck has 12 face cards because each suit has a jack, queen, and king. That makes the probability 12 out of 52, which reduces to 3 out of 13.

Formula

Probability model

P(E) = favorable outcomes / total outcomes

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