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Let X be a random variable representing the number of times you need to roll (includi

  1. Jan 1, 2008 #1
    Let X be a random variable representing the number of times you need to roll (including the last roll) a fair six-sided dice until you get 4 consecutive 6's. Find E(X)?
    answer is 1554.

    I get confused with this, probability { X > n-5 }. I know that the last for throws must be 6's and the one before 'n-4 throws' must not be a 6. Any input please?
     
  2. jcsd
  3. Jan 3, 2008 #2
    anyone?
     
  4. Jan 5, 2008 #3

    EnumaElish

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    The probability that 4 of 4 throws are all sixes is q = 1/6^4. X is distributed Geometric with success probability q, and each "trial" represents four consecutive throws.

    An alternative approach may be to calculate Prob{a 4-run of sixes} = 1 - Prob{not having a 4-run of sixes} using the binomial formula.
     
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