Probability of Independent Events With 55% Magical Coin

nflguy · 2013-01-31 08:10:07

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

bobbym · 2013-01-31 08:24:54

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.

anonimnystefy · 2013-01-31 08:26:25

Hi nflguy

Welcome to the forum!

nflguy · 2013-01-31 08:30:16

Yes I know that Bobby, I am asking how did you figure that out? What is the formula to do so?

bobbym · 2013-01-31 08:31:05

Where n is the number of heads.

nflguy · 2013-01-31 08:38:04

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?

bobbym · 2013-01-31 08:39:34

I do not use Excel but I believe there might be a command for that.

nflguy · 2013-01-31 08:42:57

bobbym wrote:

Where n is the number of heads.

Is this something I can do on a piece of paper by hand or is there a page on the website that explains it?

bobbym · 2013-01-31 08:44:13

You can use that formula for hand calculation. What part of it do you not understand?

nflguy · 2013-01-31 08:50:55

I dont know what cdot is and how to do the 4 over the n. Its been about 20 years since I learned this stuff and my memory just isn't what it used to be.

bobbym · 2013-01-31 08:53:56

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?

nflguy · 2013-01-31 08:58:14

yes I understand so far

bobbym · 2013-01-31 09:00:16

Do you know what a factorial is? For instance is 4! familiar to you or should I start right there?

nflguy · 2013-01-31 09:01:00

start right there

bobbym · 2013-01-31 09:05:27

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?

nflguy · 2013-01-31 09:07:09

got it

bobbym · 2013-01-31 09:11:24

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?

nflguy · 2013-01-31 09:14:55

yes

bobbym · 2013-01-31 09:23:41

One piece at a time:

which has a formula for it

so

which is

Okay to here?

nflguy · 2013-01-31 09:30:42

yes understand it all

bobbym · 2013-01-31 09:36:40

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!

nflguy · 2013-01-31 10:02:53

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.

bobbym · 2013-01-31 19:35:18

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.

Math Is Fun Forum

#1 2013-01-31 08:10:07

Probability of Independent Events With 55% Magical Coin

#2 2013-01-31 08:24:54

Re: Probability of Independent Events With 55% Magical Coin

#3 2013-01-31 08:26:25

Re: Probability of Independent Events With 55% Magical Coin

#4 2013-01-31 08:30:16

Re: Probability of Independent Events With 55% Magical Coin

#5 2013-01-31 08:31:05

Re: Probability of Independent Events With 55% Magical Coin

#6 2013-01-31 08:38:04

Re: Probability of Independent Events With 55% Magical Coin

#7 2013-01-31 08:39:34

Re: Probability of Independent Events With 55% Magical Coin

#8 2013-01-31 08:42:57

Re: Probability of Independent Events With 55% Magical Coin

#9 2013-01-31 08:44:13

Re: Probability of Independent Events With 55% Magical Coin

#10 2013-01-31 08:50:55

Re: Probability of Independent Events With 55% Magical Coin

#11 2013-01-31 08:53:56

Re: Probability of Independent Events With 55% Magical Coin

#12 2013-01-31 08:58:14

Re: Probability of Independent Events With 55% Magical Coin

#13 2013-01-31 09:00:16

Re: Probability of Independent Events With 55% Magical Coin

#14 2013-01-31 09:01:00

Re: Probability of Independent Events With 55% Magical Coin

#15 2013-01-31 09:05:27

Re: Probability of Independent Events With 55% Magical Coin

#16 2013-01-31 09:07:09

Re: Probability of Independent Events With 55% Magical Coin

#17 2013-01-31 09:11:24

Re: Probability of Independent Events With 55% Magical Coin

#18 2013-01-31 09:14:55

Re: Probability of Independent Events With 55% Magical Coin

#19 2013-01-31 09:23:41

Re: Probability of Independent Events With 55% Magical Coin

#20 2013-01-31 09:30:42

Re: Probability of Independent Events With 55% Magical Coin

#21 2013-01-31 09:36:40

Re: Probability of Independent Events With 55% Magical Coin

#22 2013-01-31 10:02:53

Re: Probability of Independent Events With 55% Magical Coin

#23 2013-01-31 19:35:18

Re: Probability of Independent Events With 55% Magical Coin

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