Multiple choice

Five coins whose faces are marked $2$ and $3$ are thrown. The chance of obtaining a total of $12$ is

  1. $\dfrac{11}{16}$
  2. $\dfrac{15}{16}$
  3. $\dfrac{5}{16}$
  4. $\dfrac{1}{16}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the number of 3s and (5-x) be the number of 2s. Total = 3x + 2(5-x) = 12. 3x + 10 - 2x = 12, so x = 2. We need 2 coins to show 3 and 3 coins to show 2. Probability = 5C2 * (1/2)^2 * (1/2)^3 = 10 / 32 = 5/16.

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