Subjects probability

Two Kings Probability

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Two Kings Probability


1. **Problem Statement:** Find the probability of picking two kings when selecting 2 cards from a standard 52-card deck. 2. **Formula:** The probability of an event is given by $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ 3. **Step 1: Total number of ways to pick 2 cards from 52 cards** This is a combination problem because the order of selection does not matter. $$\binom{52}{2} = \frac{52 \times 51}{2 \times 1} = 1326$$ 4. **Step 2: Number of favorable outcomes (picking 2 kings)** There are 4 kings in the deck. Number of ways to pick 2 kings from 4 kings: $$\binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6$$ 5. **Step 3: Calculate the probability** $$\text{Probability} = \frac{6}{1326} = \frac{1}{221} \approx 0.00452$$ 6. **Interpretation:** The probability of drawing two kings in a row from a 52-card deck without replacement is approximately 0.00452 or 0.452%.