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Even sum from cards

ProbabilityEasy

A deck has cards numbered through . You draw cards uniformly at random without replacement. What is the probability that the sum of the numbers is even? Give a fraction in lowest terms.

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A whole number, a decimal, a fraction like 3/8 or a percent.

Hint

A sum is even exactly when both numbers share the same parity.

Solution
  1. The sum is even exactly when both cards are odd or both are even.
  2. Whatever the first card is, cards remain.
  3. Among them, cards have the same parity as the first card, since each parity class started with cards.
  4. So the probability is .

Answer:

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