Math Problem Statement
A standard deck of cards contains $52$ cards. These $52$ cards are arranged in a circle, at random. Find the expected number of pairs of adjacent cards that are both hearts.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Expected Value
Formulas
P(\text{heart}) = \frac{13}{52} = \frac{1}{4}
P(\text{both hearts}) = \frac{13}{52} \times \frac{12}{51}
Expected number of adjacent heart pairs = 52 \times \frac{1}{17}
Theorems
Law of Total Expectation
Suitable Grade Level
Grades 10-12