Multiple choice

$A$ and $B$ throw a pair of dice. If $A$ throws $9$, find $B's$ chance throwing a higher number.

  1. $\dfrac {1}{6}$
  2. $\dfrac {5}{6}$
  3. $\dfrac {1}{36}$
  4. $\dfrac {35}{36}$
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A Correct answer
Explanation

A throws 9. The possible outcomes for A are (3,6), (4,5), (5,4), (6,3). B needs to throw a sum > 9, which is 10, 11, 12. Outcomes for B: (4,6), (5,5), (6,4), (5,6), (6,5), (6,6). Total 6 outcomes out of 36. Probability = 6/36 = 1/6.

AI explanation

When two dice are thrown, the total number of outcomes is 36. B needs to throw a sum higher than 9, meaning the sum must be 10, 11, or 12. The favorable outcomes are (4,6), (5,5), (6,4), (5,6), (6,5), and (6,6), totaling 6 outcomes. The probability is 6 divided by 36, which equals 1/6. The result is 1/6.

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