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#1 2013-02-01 07:10:07
- nflguy
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Probability of Independent Events With 55% Magical Coin
Lets say I have a magical coin that lands on heads 55% of the time and tails the other 45% of the time. How could I figure out how often out of 4 flips it will land on heads 0,1,2,3,4 times?
I have figured out that
4 heads is 9.15% (.55 * .55 * .55 * .55)
0 heads is 4.10% (.45 * .45 * .45 * .45)
I know that the answer is for 3 heads is 29.95%, 1 heads is 20.05% and 2 heads is 36.75%.
The problem is I can't figure out the formula for those. I was able to get the 3 heads using (0.55*0.55*0.55*0.45)*4 and the 1 heads by using (0.55*0.45*0.45*0.45)*4 but I dont even know if that is the right way to do it, and what the reason is that I have to use * 4 for those but the first two. I still can't figure out the 2 heads formula I just subtracted the other values to get the number.
I would like to be able to do this using other values and numbers of flips so the explanation and formula to do this one would greatly help me out.
Tom
#2 2013-02-01 07:24:54
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Hi;
Just one heads is 20.0475%
Just 2 heads is 36.753 %
Just 3 heads is 29.9475 %
You could use the binomial distribution.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2013-02-01 07:26:25
- anonimnystefy
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Re: Probability of Independent Events With 55% Magical Coin
Hi nflguy
Welcome to the forum! 
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#5 2013-02-01 07:31:05
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Where n is the number of heads.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2013-02-01 07:38:04
- nflguy
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Re: Probability of Independent Events With 55% Magical Coin
Ah ok so this is a binomial problem, sadly I am not that familiar with how they work. Ill have to go back and read up on the website to try and understand them a little more. Can you do binomial formulas in excel?
#7 2013-02-01 07:39:34
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
I do not use Excel but I believe there might be a command for that.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#9 2013-02-01 07:44:13
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
You can use that formula for hand calculation. What part of it do you not understand?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#11 2013-02-01 07:53:56
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
That little dot in front means multiplication.
(.55)^n means raise .55 to the power of the number of heads.
Is an nCr or a binomial coefficient. The definition depends on a factorial, do you follow so far?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#13 2013-02-01 08:00:16
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Do you know what a factorial is? For instance is 4! familiar to you or should I start right there?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#15 2013-02-01 08:05:27
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Mathematicians are real big on two things, jargon and notation. They figure that way no one knows what they are talking about and that is the way they like it.
4! pronounced 4 factorial is shorthand for 4 x 3 x 2 x 1.
3! is 3 x 2 x 1
8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Okay?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#17 2013-02-01 08:11:24
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Let's go back to that magical formula:
and do one. Let's say you wanted just 2 heads out of 4 tosses. We know that n is the number of heads.
Do you follow the plugging in of 2 into the formula?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#19 2013-02-01 08:23:41
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
One piece at a time:
which has a formula for it
so
which is
Okay to here?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#21 2013-02-01 08:36:40
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Then lets put it all together:
yes understand it all
Are you a programmer because they are much quicker than math types when it comes to understanding math!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#22 2013-02-01 09:02:53
- nflguy
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Re: Probability of Independent Events With 55% Magical Coin
No programmer but I know HTML and dabble in sql server and I catch on quick to things especially topics that intrigue me. I am the type of person that will use the excel functions for efficiency but I want to be able to know how to do it just for the knowledge. Hell I was playing around taking quizzes last night on your site just for the fun on it.
I was always good at math in school but I dropped out before my junior year to start working so I am pretty sure I didn't learn this. I kick myself now because the things I am interested in now math, science, history are all things I didn't pay much attention in school. This may sound silly to some but I actually look forward to my kids bringing home school work asking for help because I want to relearn everything. Anyway I really appreciate the help and the thorough explanation.
BTW I did find the formula on excel for those future readers that want to check their work in excel
=BINOMDIST(2,4,0.55, FALSE)
2 is successes
4 is trials
.55 is probability
true or false is for if probability is cumulative.
#23 2013-02-01 18:35:18
- bobbym
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Re: Probability of Independent Events With 55% Magical Coin
Hi;
This forum is a very good place for you to learn and share mathematics.
I like the idea that you try to use computer math to learn about math. You will only have to use half your wits as I do to succeed.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.