fiftythree
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#1
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Im really stuck on this question

Three dice are thrown. Find the probability of obtaining different scores on all the dice.

The answer is 0.5556 but i cant get anywhere near this..
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RDKGames
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(Original post by fiftythree)
Im really stuck on this question

Three dice are thrown. Find the probability of obtaining different scores on all the dice.

The answer is 0.5556 but i cant get anywhere near this..
For them all to take different values, the first die has 6 options. The second die has 5 options, and the third die has 4 leftover options.

The total number of ways in which we have a resulting roll where all three dice have different numbers is precisely 6 x 5 x 4 ... or if you will, (6 P 3) which denotes the number of ways we can pick 3 numbers out of 6 where order matters.

Now you just need to obtain the probability of rolling a particular combination.

Then multiply this by (6 P 3) as this imposes that your probability concerns only the cases where we roll three distinct numbers.
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ThiagoBrigido
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(Original post by RDKGames)
For them all to take different values, the first die has 6 options. The second die has 5 options, and the third die has 4 leftover options.

The total number of ways in which we have a resulting roll where all three dice have different numbers is precisely 6 x 5 x 4 ... or if you will, (6 P 3) which denotes the number of ways we can pick 3 numbers out of 6 where order matters.

Now you just need to obtain the probability of rolling a particular combination.

Then multiply this by (6 P 3) as this imposes that your probability concerns only the cases where we roll three distinct numbers.
Would that not be (6/6)x(5/6)x(4/6)?
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fiftythree
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(Original post by RDKGames)
For them all to take different values, the first die has 6 options. The second die has 5 options, and the third die has 4 leftover options.

The total number of ways in which we have a resulting roll where all three dice have different numbers is precisely 6 x 5 x 4 ... or if you will, (6 P 3) which denotes the number of ways we can pick 3 numbers out of 6 where order matters.

Now you just need to obtain the probability of rolling a particular combination.

Then multiply this by (6 P 3) as this imposes that your probability concerns only the cases where we roll three distinct numbers.
Sorry im still confused. I get that theres 120 ways of rolling the 3 dice so that they show different scores.

But what do u mean by "Now you just need to obtain the probability of rolling a particular combination."
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RDKGames
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(Original post by fiftythree)
Sorry im still confused. I get that theres 120 ways of rolling the 3 dice so that they show different scores.

But what do u mean by "Now you just need to obtain the probability of rolling a particular combination."
Consider an arbitrary combination. Eg. (1,2,5)

What is the probability that this combination is obtained?

This is what I mean.




Anyway, for an alternative train of thought, what is the probability that the first die lands on any number? What is the probability that the second die lands on any number EXCEPT the same number as the last die? What is the probability that the third die lands on any number EXCEPT on those taken by the last two dice? Multiply these probs together.
Last edited by RDKGames; 4 weeks ago
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RDKGames
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(Original post by ThiagoBrigido)
Would that not be (6/6)x(5/6)x(4/6)?
Yes it's exactly that.
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fiftythree
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(Original post by RDKGames)
Consider an arbitrary combination. Eg. (1,2,5)

What is the probability that this combination is obtained?

This is what I mean.
thanks i got it.
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