SOLUTION: In the game of Clue, the guilty person can be chosen from 6 people, and there are 9 differente possible weapons, and 9 possible rooms. What is the probability of making a random gu

Question 1015572: In the game of Clue, the guilty person can be chosen from 6 people, and there are 9 differente possible weapons, and 9 possible rooms. What is the probability of making a random guess of who the guilty person is, the location, the murder weapon and the guess being correct?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
well, you've got 6 people and for each of those 6 people you've got 9 weapons, and for each of those weapons, you've got 9 rooms.

total of all possibilities is 6 * 9 * 9 = 486.

since only one of those possibilities is the correct one, then the probability of guessing the correct one randomly is 1/486.

to see how this works, consider 2 people and 2 weapons and 2 rooms.

the total possibilities are 2*2*2 = 8.

if you let a = one person and b equal to the other person and x = one weapon and y be another weapon and 1 = the first room and 2 = the second room, then the total possibilities are:

ax1
ax2
ay1
ay2
bx1
bx2
by1
by2

out of those 8 possibilities, only one will be the correct one, so just guessins gets you a probability of success of 1/8.

it works the same way with 6 people and 9 weapons and 9 rooms, except there's too many to list, so you rely on the formula.

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