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Forgot basic probability stuff

  1. Jan 9, 2007 #1
    1. The problem statement, all variables and given/known data

    coin tossed 70 times, find exact value for probability that number of heads is between 35 and 55

    2. Relevant equations

    NA

    3. The attempt at a solution

    P(heads) = 1/2;
    and then I am not sure....

    edit: ok, maybe something like this:
    (1/2)*(35/70) - (1/2)*(55/70) ?? could someone confirm/correct?

    Thanks in advance.
     
    Last edited: Jan 9, 2007
  2. jcsd
  3. Jan 9, 2007 #2

    Dick

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    edit: ok, maybe something like this:
    (1/2)*(35/70) - (1/2)*(55/70) ?? could someone confirm/correct?

    Not even close. Try 'what is the probability of exactly 35' first. Hint: how many ways can this happen? Hint: what is the probability of each 'way'? Hint: Combinatorial coefficients. Ring a bell?
     
  4. Jan 9, 2007 #3
    n!/(k!(n-k)!) with n = 70, k = 35
    1/2, so you multiply the above equation by 1/2?
    somewhat, but do you mind giving general approach after 'what is the probability of exactly 35'? this is not too complicated of a problem, I just got "rusty" after a year.

    Thank you again.
     
  5. Jan 9, 2007 #4

    Dick

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    You are getting there. But you don't multiply by 1/2. You need to get exactly 35 head s and 35 tails. So the odds of one such event is (1/2)^35*(1/2)^35. After you've get the answer for 35 then you should be able to do 36,37,...,55. Add them up!
     
  6. Jan 9, 2007 #5

    radou

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    The coin-tossing experiment is a typical example of a discrete random variable X given with the binomial distribution, i.e. for a given number of trials, say n, and a probability p of each trial, the probability that an outcome with the probability p occurs k times is given with [tex]p(X=k)=\left( \begin{array}{cc} n\\ k \end{array} \right)=p^k(1-p)^{n-k}[/tex].
     
    Last edited: Jan 9, 2007
  7. Jan 9, 2007 #6

    HallsofIvy

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    Of course, you will have to calculate
    [tex]\left(\begin{array}{c}70 \\ i\end{array}\right)\frac{1}{2^{70}}[/tex]
    for every i from 35 to 55 and sum.

    If the problem had not said "find the exact value", I would have suggested using a normal approximation.
     
  8. Jan 10, 2007 #7

    Dick

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    Maybe part of the exercise is to instill a genuine fondness for normal distributions.
     
  9. Jan 10, 2007 #8
    well the second part actually asks to find approximate value with continuity correction. I was thinking of using Central Limit theorem? or what should I use?
    ps: sorry if my answers are dumb, this is a beginning of a second probability course and these are review excersizes; something is coming back to me but it's all mixed in my head ....
     
  10. Jan 10, 2007 #9

    Dick

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    These are cookbook exercises. No theorems, please. The binomial distribution you've just been working with can be approximated by a normal distribution. What are it's mean and std deviation? Look it up. So now you just can do the approximation by getting area under the normal curve (from a table or computer). Between what limits? Now look up continuity correction.
     
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