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Forgot basic probability stuff

  • Thread starter EvLer
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1. Homework Statement

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

2. Homework 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.
 
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Answers and Replies

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?
 
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Not even close. Try 'what is the probability of exactly 35' first. Hint: how many ways can this happen?
n!/(k!(n-k)!) with n = 70, k = 35
Hint: what is the probability of each 'way'?
1/2, so you multiply the above equation by 1/2?
Hint: Combinatorial coefficients. Ring a bell?
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.
 
Dick
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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.
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!
 
radou
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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.
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].
 
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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.
 
Dick
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Maybe part of the exercise is to instill a genuine fondness for normal distributions.
 
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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 ....
 
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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