Forgot basic probability stuff

In summary, the probability of heads on seventy coin tosses is 1/2. The approximate value for this probability is found by multiplying 1/2 by the number of heads, 35 in this case, and adding 1/2 to this value for the number of tails, 35+1.
  • #1
EvLer
458
0

Homework Statement



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

Homework Equations



NA

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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  • #2
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?
 
  • #3
Dick said:
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
Dick said:
Hint: what is the probability of each 'way'?
1/2, so you multiply the above equation by 1/2?
Dick said:
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.
 
  • #4
EvLer said:
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!
 
  • #5
EvLer said:
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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  • #6
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.
 
  • #7
Maybe part of the exercise is to instill a genuine fondness for normal distributions.
 
  • #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 ...
 
  • #9
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.
 

1. What is probability?

Probability is a measure of the likelihood or chance that a certain event will occur. It is usually expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty.

2. What is the difference between probability and odds?

Probability and odds are both ways of measuring the likelihood of an event, but they are calculated differently. Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes, while odds are the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

3. What is the difference between independent and dependent events?

Independent events are events that do not affect each other's probability, meaning the outcome of one event does not influence the outcome of the other. Dependent events, on the other hand, are events where the outcome of one event does affect the probability of the other.

4. How do you calculate the probability of multiple events occurring?

The probability of multiple events occurring is calculated by multiplying the probabilities of each individual event. This is known as the multiplication rule of probability.

5. What is the difference between theoretical and experimental probability?

Theoretical probability is the probability of an event based on mathematical calculations and assumptions, while experimental probability is the probability of an event based on actual observations and data. Theoretical probability is what we expect to happen, while experimental probability is what actually happens in practice.

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