Multiple choice

If four dice are thrown together, then the probability that the sum of the numbers appearing on them is 13 is

  1. $\displaystyle \frac{5}{216}$
  2. $\displaystyle \frac{35}{324}$
  3. $\displaystyle \frac{11}{432}$
  4. $\displaystyle \frac{11}{216}$
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B Correct answer
Explanation

The total outcomes for four dice is 6^4 = 1296. The number of ways to get a sum of 13 with four dice is 140. The probability is 140/1296 = 35/324.

AI explanation

When four dice are thrown, the total number of possible outcomes is 6^4, which equals 1296. The total number of favorable outcomes where the sum is exactly 13 is given by the coefficient of x^13 in the expansion of (x plus x^2 plus x^3 plus x^4 plus x^5 plus x^6)^4, which is 140. The required probability is therefore 140 divided by 1296, which simplifies to 35/324.

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