# Forgot basic probability stuff

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

and then I am not sure....

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

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Dick
Homework Helper
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?

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
Homework Helper
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!

Homework Helper
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 $$p(X=k)=\left( \begin{array}{cc} n\\ k \end{array} \right)=p^k(1-p)^{n-k}$$.

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HallsofIvy
Homework Helper
Of course, you will have to calculate
$$\left(\begin{array}{c}70 \\ i\end{array}\right)\frac{1}{2^{70}}$$
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
Homework Helper
Maybe part of the exercise is to instill a genuine fondness for normal distributions.

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