The probability of getting a sum of 9 when two dice are thrown is 19\frac{1}{9}91​.

Quick Scoop

Step 1: Total possible outcomes

When two fair six‑sided dice are thrown (or one die thrown twice), each die has 6 faces, so the total number of ordered outcomes is:

  • 6×6=366\times 6=366×6=36 equally likely possibilities.

Step 2: Outcomes that give sum 9

List all ordered pairs (first throw,second throw)(\text{first throw},\text{second throw})(first throw,second throw) whose sum is 9:

  • (3, 6)
  • (4, 5)
  • (5, 4)
  • (6, 3)

So there are:

  • 4 favorable outcomes out of 36.

Step 3: Compute the probability

P(sum=9)=favorable outcomestotal outcomes=436=19P(\text{sum}=9)=\frac{\text{favorable outcomes}}{\text{total outcomes}}=\frac{4}{36}=\frac{1}{9}P(sum=9)=total outcomesfavorable outcomes​=364​=91​

So, if someone asks “what is the probability of getting a sum 9 from two throws of a dice?”, the compact answer is:

  • \boxed{\frac{1}{9}\approx 0.111\text{ (about 11.1%)}}.

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