PROBABILITY

[kwame.appau]

Hi am confused as to how to solve this probability question

What is the probability of getting at least one 5 and one 6 when you roll 3 dices?

the wording "at least one 5 and one 6 " confuses me. Does the "at least apply only to 5 or to both 5 and 6 in the question above?

Please I need clarification and how to solve this.
Thanks

[tommywallach]

Hey Kwame,

Where is this question from? This is much harder than any probability questions I've ever seen on the GRE. This would NEVER appear on the GRE.

It seems to be the question is saying you need to get one 5 and one 6, and it doesn't matter what the other die is (it could be another 5 or another 6 or some other number).

The odds of getting a 5 on the first throw: 1/6

The odds of getting a 6 on the second throw: 1/6

The odds of getting a 5 and a 6 in two throws: 1/36

But we have three throws, so that two throw combo could go any of 6 places:

_56
_65
5_6
6_5
56_
65_

Each of these is 1/36 chance, and there are 6 of them, so 1/36 is the odds of getting at least one 5 and one 6.

-t

P.S. You could also think of it this way, there are 36 ways to roll three dice (if we IGNORE order):

(6 * 6 * 6)/3! = 36

How many of those have one 5 and one 6?

156
256
356
456
556
656

That's 6/36 = 1/6