What is the probability of drawing a king from a standard deck of 52 cards?

Step-by-step solution

1. 1

   Check that the outcomes are equally likely. A single card drawn from a well-shuffled standard deck gives $52$ outcomes with the same chance each, so the classical rule $P=\dfrac{\text{favourable}}{\text{total}}$ applies directly — no conditioning or counting formulas are needed.

2. 2

   Count the favourable outcomes. A standard deck has four suits, and each suit contains exactly one king, so there are

   $4\ \text{kings}$

3. 3

   Form and reduce the ratio.

   $P(\text{king})=\frac{4}{52}=\frac{1}{13}$

   Dividing numerator and denominator by $4$ gives the exact answer as a single unit fraction.

4. 4

   Express it as a decimal and a percentage.

   $\frac{1}{13}=0.076923\ldots\approx 7.69\%$

   So roughly one draw in thirteen is a king.

5. 5

   Cross-check through the odds. There are $4$ kings and $52-4=48$ non-kings, so the odds in favour are $4:48=1:12$. Converting odds to probability,

   $P=\frac{1}{1+12}=\frac{1}{13}\ \checkmark$

   A second check is the complement: $P(\text{not king})=\tfrac{48}{52}=\tfrac{12}{13}$, and $\tfrac{1}{13}+\tfrac{12}{13}=1$.