Multiple choice

Two cards are drawn at random from $10$ cards numbered $1$ to $10$. The probability that their sum is even if both the cards are drawn together

  1. $\displaystyle \frac{1}{3}$
  2. $\displaystyle \frac{4}{9}$
  3. $\displaystyle \frac{5}{9}$
  4. $\displaystyle \frac{1}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ways to pick 2 cards from 10 is 10C2 = 45. To get an even sum, both cards must be even (5C2 = 10 ways) or both must be odd (5C2 = 10 ways). Total favorable = 20. Probability = 20/45 = 4/9.

AI explanation

The total number of ways to draw 2 cards from 10 is 10C2, which equals 45. The sum is even if both cards are even or both are odd, giving 5C2 plus 5C2, which equals 20 favorable outcomes. The probability is the ratio of favorable outcomes to total outcomes, which is 20/45 or 4/9.

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