+ Reply to Thread
Results 1 to 6 of 6

Thread: probability of 8 successes out of 256 events

  1. #1
    Points: 1,765, Level: 24
    Level completed: 65%, Points required for next Level: 35

    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    probability of 8 successes out of 256 events




    Hi all hope you are well, i was trying to calculate what the probability of getting exactly 8 successes in 256 events. I used a Binomial on line calculator but the result just didnt look right

    There are 2 outcomes so it is like a coin toss so put these values in

    Probability of success on a single trial - 0.5
    Number of trials - 256
    Number of successes (x) - 8

    and got the result - 3.53792472330638E-63

    if the sequence is broken then we start from 1 again so H,H,H,H,H,T is a lossing sequence and we start again from 1 but 6 of the 256 tries has been used now

    Hope this makes sense

    Thank you

  2. #2
    Points: 4,841, Level: 44
    Level completed: 46%, Points required for next Level: 109
    Con-Tester's Avatar
    Posts
    167
    Thanks
    3
    Thanked 59 Times in 57 Posts

    Re: probability of 8 successes out of 256 events

    If I understand your question correctly, you want to know the probability of getting at least eight consecutive successes in a run of up to 256 trials, where the probability of a success on a single trial is 0.5. Is that correct?

    If so, it would mean that the run ends as soon as either (1) you have eight consecutive successes, or (2) you have done 256 trials. Is that also correct?

  3. #3
    Points: 1,765, Level: 24
    Level completed: 65%, Points required for next Level: 35

    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: probability of 8 successes out of 256 events

    Yes that is correct.thank you

  4. #4
    Points: 1,765, Level: 24
    Level completed: 65%, Points required for next Level: 35

    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: probability of 8 successes out of 256 events

    Also I would like to know probability that at least on series of 8 consecutive success occur when all 256 events are completed. Thank you

  5. #5
    Points: 1,765, Level: 24
    Level completed: 65%, Points required for next Level: 35

    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: probability of 8 successes out of 256 events

    HI Can anyone help me with this if not can you suggest another forum that might be able to answer my question. Thank you

  6. #6
    Points: 4,841, Level: 44
    Level completed: 46%, Points required for next Level: 109
    Con-Tester's Avatar
    Posts
    167
    Thanks
    3
    Thanked 59 Times in 57 Posts

    Re: probability of 8 successes out of 256 events


    The probability is 0.391316, which is borne out by a Monte Carlo simulation of over 100,000,000 trials.

    The probability generating function is:

    P_{n+1} = P_n + \frac{1 - P_{n - 8}}{2^9}

    with

    P_1 = P_2 = P_3 = P_4 = P_5 = P_6 = P_7 = 0

    and

    P_8 = \frac{1}{2^8}.


    You want P_{256}.

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats