One dice is rolled three times. What is the probability of getting at least one four?

I've been getting stuck on what to do next I know that it could be one four, two fours, or all three rolls could be fours. I just don't know which probability to use 1/216, 5/216, or 25/216? Or if any of those are correct?

  • 1
    $\begingroup$ Welcome to Math.SE! Please consider updating your question with some information about what you have tried or where you are getting stuck. You will find people are much more willing to help if you do! $\endgroup$ – Nick Peterson Mar 4 '14 at 21:06
  • $\begingroup$ Consider the negative probability space: what is the probability of getting no fours on three consecutive rolls? $\endgroup$ – abiessu Mar 4 '14 at 21:53

What is the probability $p$ to get no 4 at all?

$1 - p $ is your answer.

  • $\begingroup$ p=5/6? So the answer would be 1-(5/6) so 1/6? $\endgroup$ – Megan Mar 4 '14 at 21:12
  • $\begingroup$ I mean no 4 at all during the 3 attempts. $\endgroup$ – mookid Mar 4 '14 at 21:13
  • $\begingroup$ (5/6)^3=p then it would be 1-(5/6)^3=91/216? $\endgroup$ – Megan Mar 4 '14 at 21:14
  • $\begingroup$ @Megan: That is correct. $\endgroup$ – Ross Millikan Mar 4 '14 at 21:16
  • $\begingroup$ @mookid Thanks so much! $\endgroup$ – Megan Mar 4 '14 at 21:16

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