Dice odds: rolling 3 or 4 dice and having 2 + numbers match

1) If I roll four six sided dice, what are the odds of me matching two of them? What are the odds of me matching three of them, and what are the odds of me matching all four of them?

2) If I roll three six sided dice, what are the odds of me matching two of them and what are the odds of me matching all three of them?

3) Please tell me how you worked it out.

Diceman

http://www.crimebuff.pwp.blueyonder.co.uk/

Re: Dice odds: rolling four dice and having two numbers matc

diceman said:

1) If I roll four six sided dice, what are the odds of me matching two of them?

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When you say “match two” do you mean exactly two matches or could there be two pair of matches?

For #2
There are 6 ways out of 216 for all three to match.
There are 90 ways out of 216 for two to match.

Yes, I mean exactly two matches but would like to know the odds of matching a pair.

For question number two. Does 6 ways out of 216 mean 36 to 1? And does 90 ways out of 216 mean 2.4 to 1?

Please could you tell me how you worked this out and what the odds are using four dice?

http://www.crimebuff.pwp.blueyonder.co.uk/

diceman said:

I mean exactly two matches but would like to know the odds of matching a pair.
For question number two. Does 6 ways out of 216 mean 36 to 1? And does 90 ways out of 216 mean 2.4 to 1?

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No the question asks for odds not probability!
You must consult your textbook for a definition. Most often it means the ratio of favorable outcomes to un-favorable outcomes.

If you toss four dice there are 6<SUP>4</SUP> outcomes.
Exactly two matches happen in 720 ways.
Exactly three matches happen in 120 ways.
Four matches happen in 6 ways.