# simple probability question - for someone I'm sure

Discussion in 'Mathematics' started by beedge, Feb 5, 2011.

1. ### beedgeNew commenter

What's the best way of working of working out the following questions:

I roll 2 dice - what's the probability that (at least) 1 of them is higher than a 2?

I roll 7 dice, - what's the probability that (at least) 1 of them is higher than 2?

I roll n dice - what's the..... you get the idea.

Thank you

2. ### beedgeNew commenter

What's the best way of working of working out the following questions:

I roll 2 dice - what's the probability that (at least) 1 of them is higher than a 2?

I roll 7 dice, - what's the probability that (at least) 1 of them is higher than 2?

I roll n dice - what's the..... you get the idea.

Thank you

3. ### DMNew commenter

Work out the probability of all of the dice showing 1 (I am hoping you know how to do this but just say if you don't) and then subtract this answer from 1.

4. ### DMNew commenter

Ah I thought that said a 2 or higher but the same principle applies. Start with 2 dice, then consider 3 dice, 4 dice etc. It won't take long for you to see what is going on.

5. ### DMNew commenter

Writing down a few lines of Pascal's triangle might help too ...

6. ### D Franklin

I don't think you should need it; the key point here is that if "at least 1 of them is higher than a 2" if and only iff "all of them are smaller than a 3" is false. And of course, it's easy to find the probabilty that all of them are smaller than 3.

7. ### beedgeNew commenter

Got it.

So, if you want to know the probability that after rolling n dice, at least 1 of them is higher than a 2 (i.e. a 3 or more), you just need to say:

1 - (2/6)^n

8. ### DMNew commenter

That's the right answer beedge but I thought it was easiest (and you asked for the easiest method) to see that the sum of the rows of Pascal's triangles gave you 2 to the power of something and the total number of outcomes was 3 to the power of something blah blah.

9. ### DMNew commenter

I mean 6 to the power of something!