### Brain Teasers

# Get a Clue

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

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?

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

### Answer

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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## Comments

Aug 16, 2004

i guess

This teaser is incorrect. Probablility is added. 1/6 + 1/6 + 1/9. The odds are 25/54 of getting at least one correct. You are correct in the number of possible right and wrong combinations but some winning combinations are easier to achieve than other winning or losing combinations. Many people dont understand this concept but you can concure this with any math professor.

"some winning combinations are easier to achieve than other winning or losing combinations."??? What do you mean by this? Every combination is equally likely to have occured. Besides, by merely adding 1/6, 1/6, and 1/9, you are counting the combinations that get two right twice and the one that gets all three right three times. In order to do it by adding, you would have to add all the odds of getting one right, then subtract the odds of getting two right (to reduce each to counting it once), then add the odds of getting all three right (since subtracting each two once subtracted the three three times, which is one time too many - it got removed completely!), making 1/6+1/6+1/9-1/36-1/54-1/54+1/324. When you do the math with a calculator, it comes out as 31/81. Don't believe me? Try it - then multiply the answer by 81 to get 31.

Not true. I am an authority in probability and event calculations. Your formula is incorrect. It is 1/6 + 1/6 + 1/9. How do I know this? Its how I make a living. Since I'm not living in a cardboard box and my family is not hungry, I must be doing something right.

By the way, you can calculate this problem as if you had two 6-sided dice and one 9-sided die.

Since you probably wont take my word for it, please consult someone else of mathamatical authority if you want to be enlightened. Perhaps your local COLLEGE math professor. (Even though I learned this in 6th grade first). If I seem grumpy, Im tired. No offense intended.

Sorry I wont shut up but, if you are going to use multiplication to calculate probability, you need to use the 'multiplicative rule'. You can just use the rule you made up. http://www.netnam.vn/unescocourse/statistics/46.htm

ARGGHH! Im tired. I meant you CANNOT use the rule you just made up.

I have to agree with xpitxbullx. I took an intro course in probability and statistics at Michagan State. There are proven formulas used to find these answers.

I want to apologize for being so bull-headed. Poker is correct and I was not. Great teaser because it made me test my logic and concede to the proper math.

Poker is certainly correct. A more mathematical way of expressing the answer would be:

P(not event) = 1 - P(event)

The probability of not getting them all wrong is the complement of getting at lest one right. (If you don't get them all wrong then you must have had at least one correct).

P = 1 - (5/6*5/6*8/9)

P = 1 - 200/324 = 124/324 = 31/81

Nice Puzzle Poker!

Good luck with the Vacancies coulumns Pit Bull!

P(not event) = 1 - P(event)

The probability of not getting them all wrong is the complement of getting at lest one right. (If you don't get them all wrong then you must have had at least one correct).

P = 1 - (5/6*5/6*8/9)

P = 1 - 200/324 = 124/324 = 31/81

Nice Puzzle Poker!

Good luck with the Vacancies coulumns Pit Bull!

Bravo, I'm not too bright and I got it (although it took me quite some time )

jumbo is right. There is only one combination where not at least one of the variables is right. And this combination is: The all wrong.

1-p thing learned that in 6e grade.

1-p thing learned that in 6e grade.

I calculated the probabilty of getting the first one wrong (5/6), multiplied by the chance of getting the second one wrong (5/6) and then did the same again for the last one (8/9). The answer was 61.73 - this is the chance of getting all three wrong; therefore the chance of getting at least one right is 38.27%.

Just to point out a little something that every1 seems to have overlooked. Sadly, contrary to what the guy who says statistics are how he makes his living seems to think, 1/6 + 1/6 + 1/9 is not 25/54. It turns out that 3/18 + 3/18 + 2/18 is 8/18 or 24/54. At least you were close to the wrong answer though dude.

"I am an authority in probability and event calculations. Your formula is incorrect. It is 1/6 + 1/6 + 1/9. "

Addition with probabilities is NEVER correct...

given 3 die rolls what is probability of rolling a 1?

1/6+1/6+1/6?? no

given 6 die rolls what is probabilty of rolling a 1?

1/6+1/6+1/6+1/6+1/6+1/6?? no

given 10,000 die rolls what is probabilty of rolling a 1?

1/6+1/6+1/6+.....+1/6?? no

if you are given 100 billion trillion number of dice rolls.. the probability of rolling a 1 (at least once) is STILL LESS THEN 100%

Hey slow_turtle: you say "addition with probability is NEVER correct". I say that's a load of rubbish! What's the probability of throwing a 1 or a 2 with a normal die? Well, it's prob(throwing a 1) + prob(throwing a 2) = 1/6 + 1/6 =2/6 =2/3

Never say never!

Never say never!

You can add with probability. You just have to know what to add. If you want to add the possibilities, go ahead. There are 1x6x9 possibilities that get the suspect right - that's 54. Of the ones that don't get the suspect right, there are still 5x1x9 possibilities that get the weapon right - that's 45. Of the ones that don't get the suspect or weapon right, there are still 5x5x1 possibilities that get the room right - that's 25. Add those together to get 124. So the probability is 124/324 or, reduced, 31/81.

im really rusty with math... so im probably wrong... but i was thinking... would you only use multiplication when you are figuring the probably of the combinations. sure there are a bunch of probabilty is large for combinations but we arent supposed to be thinking of that just the probability of getting 1 answer right. i also added mine like the others ...1/6+1/6+1/9.......2/6+1/9...........6/18+2/18.......8/18......or 4/9ths to be easier.... any one get anything similar???? HAHAHAH ok this teaser is going to make me go back to school

ok after thinking about it more i think im wrong.. HAHha multiplacation seems to make more sense now

a duhhhhhhhhhhhhhhh

I agree with Poker.

But it's fun looking at the comments. I'd say you'd learn more than by reading a book.

But it's fun looking at the comments. I'd say you'd learn more than by reading a book.

I just have to say it. Your all wrong, the question's wrong. The chances of someone randamly guessing are 0. In clue you always start with some cards. Therefore you will always start with some idea of what not to guess, raising your chances of getting at least one right. I'm still struggleing with the math, but I know my clue game.

I just got done reading a brain teaser that was really long so I decided i was not going to try to salve it

HAHAHA!!! My answer was:

1/8515157028618240000

1/8515157028618240000

I am no good at math, so my answer wasn't right, but great job anyways!!!

Get the answer right? I didn't even read the question right!!

thought it was 3/9s but it was a guess ...

i got 1/324

why the answer is not the same as 1-5/6*5/6*8/9.

i got 1/324 from 1/6*1/6*1/9. can anybody explain it for me?

why the answer is not the same as 1-5/6*5/6*8/9.

i got 1/324 from 1/6*1/6*1/9. can anybody explain it for me?

Brainjuice your starting point is right but your calculation is wrong. 1-5/6*5/6*8/9 is not 1/324. You have to follow the PEDMAS rules here. You have to first perform the multiplication 5/6*5/6*8/9 which will give you 200/324. When you subtract this from 1 you will get 124/324 which reduces to 31/81 on dividing both numerator and denominator by 4

That was really hard, considering i am SUPER-BAD at math!

Hmm... but if you're only trying to get one right, then take a whack at either the murderer or the weapon, and you'll have a 1/6 chance. I don't know. I won't argue about it.

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