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## Get a Clue

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #18568 Fun: (2.38) Difficulty: (2.24) Category: Probability Submitted By: Poker Corrected By: Winner4600

In Clue (called Cluedo in some countries, including its origin, England), you attempt to solve a murder mystery. There are six possible suspects, six possible weapons that the murderer could have used, and nine possible locations for the murder to have occurred.

If you guess a random suspect, a random weapon, and a random room, what is the probability of getting at least one right?

31/81.

The total number of possibilities is 324 (6*6*9). The number of completely wrong guesses is 200 (5*5*8). So the number of partially or fully correct guesses is 124 (324-200). The probability is 124 out of 324, which can be reduced to 31 out of 81.

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