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simple probability question - for someone I'm sure

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

  1. beedge

    beedge New 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. beedge

    beedge New 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. DM

    DM New 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. DM

    DM New 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. DM

    DM New commenter

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

    beedge New 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. DM

    DM New 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. DM

    DM New commenter

    I mean 6 to the power of something!
     

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